Advances in Nonlinear Dynamics: Methods and Applications

In this paper, taking the generalized synchronization problem of discrete chaotic systems as a starting point, a generalized synchronization method incorporating error-feedback coefficients into the controller based on the generalized chaos synchronization theory and stability theorem for nonlinear systems is proposed. Two discrete chaotic systems with different dimensions are constructed in this paper, the dynamics of the proposed systems are analyzed, and finally, the phase diagrams, Lyapunov exponent diagrams, and bifurcation diagrams of these are shown and described. The experimental results show that the design of the adaptive generalized synchronization system is achievable in cases in which the error-feedback coefficient satisfies certain conditions. Finally, a chaotic hiding image encryption transmission system based on a generalized synchronization approach is proposed, in which an error-feedback coefficient is introduced into the controller. Full article

In this paper, we study the spectral properties of polarobreathers, that is, breathers carrying charge in a one-dimensional semiclassical model. We adapt recently developed numerical methods that preserve the charge probability at every step of time integration without using the Born–Oppenheimer approximation, which is the assumption that the electron is not at equilibrium with the atoms or ions. We develop an algorithm to obtain exact polarobreather solutions. The properties of polarobreathers, both stationary and moving ones, are deduced from the lattice and charge variable spectra in the frequency–momentum space. We consider an efficient approach to produce approximate polarobreathers with long lifespans. Their spectrum allows for the determination of the initial conditions and the necessary parameters to obtain numerically exact polarobreathers. The spectra of exact polarobreathers become extremely simple and easy to interpret. We also solve the problem that the charge frequency is not an observable, but the frequency of the charge probability certainly is an observable. Full article

This paper studies the aperiodic sampled-data (SD) control anti-synchronization issue of chaotic nonlinear systems under the effects of input saturation. At first, to describe the simultaneous existence of the aperiodic SD pattern and the input saturation, a nonlinear closed-loop system model is established. Then, to make the anti-synchronization analysis, a relaxed sampling-interval-dependent Lyapunov functional (RSIDLF) is constructed for the resulting closed-loop system. Thereinto, the positive definiteness requirement of the RSIDLF is abandoned. Due to the indefiniteness of RSIDLF, the discrete-time Lyapunov method (DTLM) then is used to guarantee the local stability of the trivial solutions of the modeled nonlinear system. Furthermore, two convex optimization schemes are proposed to expand the allowable initial area (AIA) and maximize the upper bound of the sampling period (UBSP). Finally, two examples of nonlinear systems are provided to illustrate the superiority of the RSIDLF method over the previous methods in expanding the AIA and enlarging the UBSP. Full article

In this paper, we study the factor of the fear effect in a predator–prey model with prey refuge and a non-differentiable fractional functional response due to the group defense. Since the functional response is non-differentiable, the dynamics of this system are considerably different from the dynamics of a classical predator–prey system. The persistence, the stability and the existence of the steady states are investigated. We examine the Hopf bifurcation at the unique positive equilibrium. Direct Hopf bifurcation is studied via the central manifold theorem. When the value of the fear factor decreases and is less than a threshold ${\kappa }_H$, the limit cycle appears, and it disappears through a loop of heteroclinic orbits when the value of the fear factor is equal to a value ${\kappa }_{het}$. Full article

This work studies a two-time-scale functional system given by two jump diffusions under the scale separation by a small parameter $\epsilon \to 0$. The coefficients of the equations that govern the dynamics of the system depend on the segment process of the slow variable (responsible for capturing delay effects on the slow component) and on the state of the fast variable. We derive a moderate deviation principle for the slow component of the system in the small noise limit using the weak convergence approach. The rate function is written in terms of the averaged dynamics associated with the multi-scale system. The core of the proof of the moderate deviation principle is the establishment of an averaging principle for the auxiliary controlled processes associated with the slow variable in the framework of the weak convergence approach. The controlled version of the averaging principle for the jump multi-scale diffusion relies on a discretization method inspired by the classical Khasminkii’s averaging principle. Full article

In this article, we consider a delayed system of first-order hyperbolic differential equations. The presence of the delay term in first-order hyperbolic delay differential equations poses significant challenges in both analysis and numerical solutions. The delay term also makes it more difficult to use standard numerical methods for solving differential equations, as these methods often require that the differential equation be evaluated at the current time step. To overcome these challenges, specialized numerical methods and analytical techniques have been developed for solving first-order hyperbolic delay differential equations. We investigated and presented analytical results, such as the maximum principle and stability results. The propagation of discontinuities in the solution was also discussed, providing a framework for understanding its behavior. We presented a fractional-step method using a backward finite difference scheme and showed that the scheme is almost first-order convergent in space and time through the derivation of the error estimate. Additionally, we demonstrated an application of the proposed method to the problem of variable delay differential equations. We demonstrated the practical application of the proposed method to solving variable delay differential equations. The proposed algorithm is based on a numerical approximation method that utilizes a finite difference scheme to discretize the differential equation. We validated our theoretical results through numerical experiments. Full article

This paper deals with the problems of finite-time boundedness (FTB) and $H_{\infty }$ FTB for time-delay Markovian jump systems with a partially unknown transition rate. First of all, sufficient conditions are provided, ensuring the FTB and $H_{\infty }$ FTB of systems given by linear matrix inequalities (LMIs). A new type of partially delay-dependent controller (PDDC) is designed so that the resulting closed-loop systems are finite-time bounded and satisfy a given $H_{\infty }$ disturbance attenuation level. The PDDC contains both non-time-delay and time-delay states, though not happening at the same time, which is related to the probability distribution of the Bernoulli variable. Furthermore, the PDDC is extended to two other cases; one does not contain the Bernoulli variable, and the other experiences a disordering phenomenon. Finally, three numerical examples are used to show the effectiveness of the proposed approaches. Full article

A novel, simple, four-dimensional hyperchaotic memristor circuit consisting of two capacitors, an inductor and a magnetically controlled memristor is designed. Three parameters (a, b, c) are especially set as the research objects of the model through numerical simulation. It is found that the circuit not only exhibits a rich attractor evolution phenomenon, but also has large-scale parameter permission. At the same time, the spectral entropy complexity of the circuit is analyzed, and it is confirmed that the circuit contains a significant amount of dynamical behavior. By setting the internal parameters of the circuit to remain constant, a number of coexisting attractors are found under symmetric initial conditions. Then, the results of the attractor basin further confirm the coexisting attractor behavior and multiple stability. Finally, the simple memristor chaotic circuit is designed by the time-domain method with FPGA technology and the experimental results have the same phase trajectory as the numerical calculation results. Hyperchaos and broad parameter selection mean that the simple memristor model has more complex dynamic behavior, which can be widely used in the future, in areas such as secure communication, intelligent control and memory storage. Full article

The crane-form pipeline (CFP) system is a kind of petrochemical mechanical equipment composed of multiple rotating joints and rigid pipelines. It is often used to transport chemical fluid products in the factory to tank trucks. In order to realize the automatic alignment of the CFP and the tank mouth, the trajectory tracking control problem of the CFP must be solved. Therefore, a saturated nonsingular fast terminal sliding mode (SNFTSM) algorithm is proposed in this paper. The new sliding mode manifold is constructed by the nonsingular fast terminal sliding mode (NFTSM) manifold, saturation functions and signum functions. Further, according to the sliding mode control algorithm and the dynamic model of the CFP system, the SNFTSM controller is designed. Owing to the existence of saturation functions in the controller, the stability analysis using the Lyapunov equation needs to be discussed in different cases. The results show that the system states can converge to the equilibrium point in finite time no matter where they are on the state’s phase plane. However, due to the existence of signum functions, the control signal will produce chattering. In order to eliminate the chattering problem, the form of the controller is improved by using the boundary layer function. Finally, the control effect of the algorithm is verified by simulation and compared with the NTSM, NFTSM and SNTSM algorithms. From the comparison results, it is obvious that the controller based on the SNFTSM algorithm can effectively reduce the amplitude of the control torque while guaranteeing the fast convergence of the CFP system state error. Specifically, compared with the NFTSM algorithm, the maximum input torque can even be reduced by more than half. Full article

The local convergence analysis of the multi-step seventh order method to solve nonlinear equations is presented in this paper. The point of this paper is that our proposed study requires a weak hypothesis where the Fréchet derivative of the nonlinear operator satisfies the $\psi$-continuity condition, which thereby extends the applicability of the method when both Lipschitz and Hölder conditions fail. The convergence in this study is considered under the hypotheses on the first-order derivative without involving derivatives of the higher-order. To find a subset of the original convergence domain, a strategy is devised here. As a result, the new Lipschitz constants are at least as tight as the old ones, allowing for a more precise convergence analysis in the local convergence case. Some concrete numerical examples showing the performance of the method over some existing schemes are presented in this article. Full article

As a measure of complexity, information entropy is frequently used to categorize time series, such as machinery failure diagnostics, biological signal identification, etc., and is thought of as a characteristic of dynamic systems. Many entropies, however, are ineffective for multivariate scenarios due to correlations. In this paper, we propose a local structure entropy (LSE) based on the idea of a recurrence network. Given certain tolerance and scales, LSE values can distinguish multivariate chaotic sequences between stochastic signals. Three financial market indices are used to evaluate the proposed LSE. The results show that the $LS{E}^{FSTE100}$ and $LS{E}^{S\&P500}$ are higher than $LS{E}^{SZI}$, which indicates that the European and American stock markets are more sophisticated than the Chinese stock market. Additionally, using decision trees as the classifiers, LSE is employed to detect bearing faults. LSE performs higher on recognition accuracy when compared to permutation entropy. Full article

In this work, an adaptive dynamic surface control law for a type of strict-feedback fractional-order nonlinear system is proposed. The considered system contained input quantization and unknown external disturbances. The virtual control law is presented by utilizing a dynamic surface control approach at each step, where the nonlinear compensating term with the estimation of unknown bounded parameters is introduced to overcome the influence of unknown external disturbances and surface errors. Meanwhile, the adaptive laws of relevant parameters are also designed. In addition, an improved fractional-order nonlinear filter is developed to deal with the explosion of complexity raised by the recursive process. In the last step, an adaptive dynamic surface control law is proposed to ensure the convergence of tracking error, in which the Nussbaum gain function is applied to solve the problem of the unknown control gain generated by input quantization. Then, the fractional Lyapunov stability theory is applied to verify the stability of the proposed control law. Finally, simulation examples are given to illustrate the effectiveness of the proposed control law. Full article

At present, malware is still a major security threat to computer networks. However, only a fraction of users with some security consciousness take security measures to protect computers on their own initiative, and others who know the current situation through social networks usually follow suit. This phenomenon is referred to as conformity psychology. It is obvious that more users will take countermeasures to prevent computers from being infected if the malware spreads to a certain extent. This paper proposes a deterministic nonlinear SEIQR propagation model to investigate the impact of conformity psychology on malware propagation. Both the local and global stabilities of malware-free equilibrium are proven while the existence and local stability of endemic equilibrium is proven by using the central manifold theory. Additionally, some numerical examples and simulation experiments based on two network datasets are performed to verify the theoretical analysis results. Finally, the sensitivity analysis of system parameters is carried out. Full article

Analytically and numerically, the study examines the stability and local bifurcations of a discrete-time $SIR$ epidemic model. For this model, a number of bifurcations are studied, including the transcritical, flip bifurcations, Neimark–Sacker bifurcations, and strong resonances. These bifurcations are checked, and their non-degeneracy conditions are determined by using the normal form technique (computing of critical normal form coefficients). We use the MATLAB toolbox MatcontM, which is based on the numerical continuation method, to confirm the obtained analytical results and specify more complex behaviors of the model. Numerical simulation is employed to present a closed invariant curve emerging from a Neimark–Sacker point and its breaking down to several closed invariant curves and eventually giving rise to a chaotic strange attractor by increasing the bifurcation parameter. Full article

The advantage of fractional-order derivative has attracted extensive attention in the field of dynamics. In this paper, we investigated the stability of the fractional-order Mathieu equation under forced excitation, which is based on a model of the pantograph–catenary system. First, we obtained the approximate analytical expressions and periodic solutions of the stability boundaries by the multi-scale method and the perturbation method, and the correctness of these results were verified through numerical analysis by Matlab. In addition, by analyzing the stability of the k’T-periodic solutions in the system, we verified the existence of the unstable k’T-resonance lines through numerical simulation, and visually investigated the effect of the system parameters. The results show that forced excitation with a finite period does not change the position of the stability boundaries, but it can affect the expressions of the periodic solutions. Moreover, by analyzing the properties of the resonant lines, we found that when the points with k’T-periodic solutions were perturbed by the same frequency of forced excitation, these points became unstable due to resonance. Finally, we found that both the damping coefficient and the fractional-order parameters in the system have important influences on the stability boundaries and the resonance lines. Full article

A chain of coupled systems of Van der Pol equations is considered. We study the local dynamics of this chain in the vicinity of the zero equilibrium state. We make a transition to the system with a continuous spatial variable assuming that the number of elements in the chain is large enough. The critical cases corresponding to the Turing bifurcations are identified. It is shown that they have infinite dimension. Special nonlinear parabolic equations are proposed on the basis of the asymptotic algorithm. Their nonlocal dynamics describes the local behavior of solutions to the original system. In a number of cases, normalized parabolic equations with two spatial variables arise while considering the most important diffusion type couplings. It has been established, for example, that for the considered systems with a large number of elements, the dynamics change significantly with a slight change in the number of such elements. Full article

In multi-sensor cooperative detection systems, to reduce target threat risk caused by attack tasks and target loss risk induced by uncertain environmental factors, this paper proposes a multi-sensor scheduling method based on joint risk assessment with variable weight. Firstly, considering the target state and prior expert experience of sensor scheduling, this paper gives a new scheme of target threat risk. Then, by combining the given target threat risk and the target loss risk, this paper constructs a joint risk model to meet the diversity of risk assessment. Secondly, a variable-weighted joint risk assessment model is given based on the adaptive weight of target loss risk and target threat risk, and the optimization problem of multi-sensor scheduling is described to minimize the multi-step prediction of the variable-weighted joint risk model. Finally, this paper relaxes above the non-convex optimization problem as a subconvex problem and designs the scheme of multi-sensor scheduling, improving the rapidity and optimization of the sensor scheduling solution. The simulation results show that the proposed method can adaptively schedule sensors and accurately track targets by using minimum sensor resources. Full article

The KP hierarchy reduction method is one of the most reliable and efficient techniques for determining exact solitary wave solutions to nonlinear partial differential equations. In this paper, according to the KP hierarchy reduction technique, rational and some other semi-rational solutions to the (2 + 1)-dimensional Maccari system are investigated. It is shown that two different types of breathers can be derived, and under appropriate parameter constraints, they can be reduced to some well known solutions, involving the homoclinic orbits, dark soliton or anti-dark soliton solution. For the dark and anti-dark solution, its interaction is similar to a resonance soliton. Furthermore, by using a limiting technique, we derive two kinds of rational solutions, one is the lump and the other one is the rogue wave. After constructing these solutions, we further discuss the interactions between the obtained solutions. It is interesting that we obtain a parallel breather and a intersectional breather, which seems very surprising. Finally, we also provide a new three-state interaction, which is composed by the dark-soliton, rogue wave and breather and has never been provided for the Maccari system. Full article

We use friction to simultaneously damp and excite a pendulum system. A Froude pendulum attached to a suspension shaft is subjected to a frictional load. We investigate two types of response of the system: regular and chaotic responses, depending on the excitation frequency. A transient chaotic solution was also obtained. We identify the motions using phase portraits, Poincaré maps, and Fourier spectra. Finally, the composite multiscaled entropy was estimated for the specified cases to confirm the preliminary classification. Full article

In this paper, the adaptive finite-time control problem for fractional-order systems with uncertainties and unknown dead-zone fault was studied by combining a fractional-order command filter, radial basis function neural network, and Nussbaum gain function technique. First, the fractional-order command filter-based backstepping control method is applied to avoid the computational complexity problem existing in the conventional recursive procedure, where the fractional-order command filter is introduced to obtain the filter signals and their fractional-order derivatives. Second, the radial basis function neural network is used to handle the uncertain nonlinear functions in the recursive design step. Third, the Nussbaum gain function technique is considered to handle the unknown control gain caused by the unknown dead-zone fault. Moreover, by introducing the compensating signal into the control law design, the virtual control law, adaptive laws, and the adaptive neural network finite-time control law are constructed to ensure that all signals associated with the closed-loop system are bounded in finite time and that the tracking error can converge to a small neighborhood of origin in finite time. Finally, the validity of the proposed control law is confirmed by providing simulation cases. Full article

This paper focuses on dealing with the problem of co-designing a fuzzy-basis-dependent event generator and an asynchronous filter of fuzzy Markovian jump systems via event-triggered non-parallel distribution compensation (non-PDC) scheme. The introduction of the event-triggered non-PDC scheme can reduce the number of real-time filter gain design operations with a large computational load. Furthermore, to perform an effective relaxation process, several kinds of time-varying parameters in filter design conditions are simultaneously relaxed by utilizing two zero equalities of transition probabilities and mismatch errors. In addition, to improve the considered performance, the event generation function is established based on fuzzy-basis-dependent event weighting matrices. Full article

In this paper, we investigate the constrained optimal control problem of nonlinear multi-input safety-critical systems with uncertain disturbances and time-varying safety constraints. By utilizing a barrier function transformation, together with a new disturbance-related term and a smooth safety boundary function, a nominal system-dependent multi-input barrier transformation architecture is developed to deal with the time-varying safety constraints and uncertain disturbances. Based on the obtained transformation system, the coupled Hamilton–Jacobi–Bellman (HJB) function is established to obtain the constrained Nash equilibrium solution. In addition, due to the fact that it is difficult to solve the HJB function directly, the single critic neural network (NN) is constructed to approximate the optimal performance index function of different control inputs, respectively. It is proved theoretically that, under the influence of uncertain disturbances and time-varying safety constraints, the system states and neural network parameters can be uniformly ultimately bounded (UUB) by the proposed neural network approximation method. Finally, the effectiveness of the proposed method is verified by two nonlinear simulation examples. Full article

The stochastic resonance (SR) of a star-coupled harmonic oscillator subject to multiplicative fluctuation and periodic force in viscous media is studied. The multiplicative noise is modeled as a dichotomous noise and the memory of viscous media is characterized by a fractional power kernel function. By using the Shapiro–Loginov formula and Laplace transform, we obtain the analytical expressions of the first moment of the steady-state response and study the relationship between the system response and the system parameters in the long-time limit. The simulation results show the nonmonotonic dependence between the response output gain and the input signal frequency, the noise parameters of the system, etc., which indicates that the bona fide resonance and the generalized SR phenomena appear. Furthermore, the fluctuation noise, the number of particles, and the fractional order work together, producing more complex dynamic phenomena compared with the integral-order system. In addition, all the theoretical analyses are supported by the corresponding numerical simulations. We believe that the results that we have found may be a certain reference value for the research and development of the SR. Full article

Today, with the rapid development of the Internet, improving image security becomes more and more important. To improve image encryption efficiency, a novel region of interest (ROI) encryption algorithm based on a chaotic system was proposed. First, a new 1D $e^{\lambda }$-cos-cot (1D-ECC) with better chaotic performance than the traditional chaotic system is proposed. Second, the chaotic system is used to generate a plaintext-relate keystream based on the label information of a medical image DICOM (Digital Imaging and Communications in Medicine) file, the medical image is segmented using an adaptive threshold, and the segmented region of interest is encrypted. The encryption process is divided into two stages: scrambling and diffusion. In the scrambling stage, helical scanning and index scrambling are combined to scramble. In the diffusion stage, two-dimensional bi-directional diffusion is adopted, that is, the image is bi-directionally diffused row by column to make image security better. The algorithm offers good encryption speed and security performance, according to simulation results and security analysis. Full article

It is well known that multicomponent integrable systems provide a method for analyzing phenomena with numerous interactions, due to the interactions between their different components. In this paper, we derive the multicomponent higher-order Chen–Lee–Liu (mHOCLL) system through the zero-curvature equation and recursive operators. Then, we apply the trace identity to obtain the bi-Hamiltonian structure of mHOCLL system, which certifies that the constructed system is integrable. Considering the spectral problem of the Lax pair, a related Riemann–Hilbert (RH) problem of this integrable system is naturally constructed with zero background, and the symmetry of this spectral problem is given. On the one hand, the explicit expression for the mHOCLL solution is not available when the RH problem is regular. However, according to the formal solution obtained using the Plemelj formula, the long-time asymptotic state of the mHOCLL solution can be obtained. On the other hand, the N-soliton solutions can be explicitly gained when the scattering problem is reflectionless, and its long-time behavior can still be discussed. Finally, the determinant form of the N-soliton solution is given, and one-, two-, and three-soliton solutions as specific examples are shown via the figures. Full article

In this paper, a wind energy conversion system is studied to improve the conversion efficiency and maximize power output. Firstly, a nonlinear state space model is established with respect to shaft current, turbine rotational speed and power output in the wind energy conversion system. As the wind velocity can be descried as a non-Gaussian variable on the system model, the survival information potential is adopted to measure the uncertainty of the stochastic tracking error between the actual wind turbine rotation speed and the reference one. Secondly, to minimize the stochastic tracking error, the control input is obtained by recursively optimizing the performance index function which is constructed with consideration of both survival information potential and control input constraints. To avoid those complex probability formulation, a data driven method is adopted in the process of calculating the survival information potential. Finally, a simulation example is given to illustrate the efficiency of the proposed maximum power point tracking control method. The results demonstrate that by following this method, the actual wind turbine rotation speed can track the reference speed with less time, less overshoot and higher precision, and thus the power output can still be guaranteed under the influence of non-Gaussian wind noises. Full article

In this paper, a robust trajectory tracking control method with state constraints and uncertain disturbances on the ground of adaptive dynamic programming (ADP) is proposed for nonlinear systems. Firstly, the augmented system consists of the tracking error and the reference trajectory, and the tracking control problems with uncertain disturbances is described as the problem of robust control adjustment. In addition, considering the nominal system of the augmented system, the guaranteed cost tracking control problem is transformed into the optimal control problem by using the discount coefficient in the nominal system. A new safe Hamilton–Jacobi–Bellman (HJB) equation is proposed by combining the cost function with the control barrier function (CBF), so that the behavior of violating the safety regulations for the system states will be punished. In order to solve the new safe HJB equation, a critic neural network (NN) is used to approximate the solution of the safe HJB equation. According to the Lyapunov stability theory, in the case of state constraints and uncertain disturbances, the system states and the parameters of the critic neural network are guaranteed to be uniformly ultimately bounded (UUB). At the end of this paper, the feasibility of the proposed method is verified by a simulation example. Full article

In this paper, a new adaptive critic design is proposed to approximate the online Nash equilibrium solution for the robust trajectory tracking control of non-zero-sum (NZS) games for continuous-time uncertain nonlinear systems. First, the augmented system was constructed by combining the tracking error and the reference trajectory. By modifying the cost function, the robust tracking control problem was transformed into an optimal tracking control problem. Based on adaptive dynamic programming (ADP), a single critic neural network (NN) was applied for each player to solve the coupled Hamilton–Jacobi–Bellman (HJB) equations approximately, and the obtained control laws were regarded as the feedback Nash equilibrium. Two additional terms were introduced in the weight update law of each critic NN, which strengthened the weight update process and eliminated the strict requirements for the initial stability control policy. More importantly, in theory, through the Lyapunov theory, the stability of the closed-loop system was guaranteed, and the robust tracking performance was analyzed. Finally, the effectiveness of the proposed scheme was verified by two examples. Full article

The research background is the elastic ring squeeze film damper. Four contact pressure models were established by analyzing the structural characteristics and movement, combined with the sliding bearing theory, including structural parameters and eccentricities. Multi-structure and multi-interval dynamic boundary conditions were selected by analyzing actual structures. Simpson, polynomial, and integrated parameters methods extended Booker formulas. By combining existences and forms of the solution and mean-value theories, approximate analytical solutions of the finite length bearing were obtained under different contacts. Combined with the short and long bearing, general structures and expressions of analytical solutions of oil film pressures and forces under three approximation theories were obtained. The oil film characteristics of the dynamic equilibrium state were obtained, and the correctness was verified by theoretical comparison. Numerical simulations analyzed the relationship among relevant parameters. It provided a theoretical basis upon which to study the geometric form, motion state, and the approximate analytical solution of the ERSFD dynamic model, and increased its research ability. Full article

In this study, new asymptotic properties of positive solutions of the even-order neutral delay differential equation with the noncanonical operator are established. The new properties are of an iterative nature, which allows it to be applied several times. Using these properties, we obtain new criteria to exclude a class from the positive solutions of the studied equation, using the comparison principles. Full article

A dynamic aircraft system conflict (concurrent event) situation exists when a time with a loss (-es) of separation (LOS) in their true or predicted trajectories is determined. Regional air traffic management (ATM) programs aim to make ATM safer and more efficient through a higher level of automation for such processes as dynamic aircraft systems concurrent events detection and, consequently, resolution. Therefore, wind and aircraft speed uncertainty parameters should be properly addressed. This paper offers an approach to a dynamic aircraft system flying under a certain concurrent event situation and demonstrates situation stochastic distribution results (output) based on determined wind speed values (while wind direction angles and the dynamic aircraft system speed values are random). Based on these facts, the stochastic dynamic aircraft system conflict distribution information under determined and random parameters might be retrieved at any specific (preferred) time moment. The observations of this study disclosed that such stochastic output data might have a certain impact on safety matters (potential “domino effect” conflicts on a horizontal plane) and on the efficiency (i.e., flight distance which eventually is a determinant of flight time, fuel costs, delays, emissions, monitoring, etc.). Full article

In this work, we analyze the asymptotic behavior of the solutions for a thermosyphon model where a binary fluid is considered, a fluid containing a soluble substance, and the Reynold’s number is large. The presented results are a generalization, in some sense, of the results for a fluid with only one component provided in Velázquez 1994 and RodrÍguez-Bernal and Van Vleck 1998. We characterize the conditions under which a fast time-dependent solution exits and it is attracted towards a fast stationary solution as the Reynold’s number tends to infinity. Numerical experiments were performed in order to illustrate the theoretical results. Using numerical simulations, we found fast time-dependent solutions close enough to the fast stationary one for certain values of the parameters. Full article