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3 pages, 183 KiB

Open AccessEditorial

Symmetry in Nonlinear Dynamics and Chaos

by Sergio Elaskar

Symmetry 2023, 15(1), 102; https://doi.org/10.3390/sym15010102 - 30 Dec 2022

Cited by 1 | Viewed by 805

Abstract

Nonlinear dynamics and chaos have collaborated to increase our understanding of several phenomena [...] Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos)

Research

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22 pages, 2399 KiB

Open AccessFeature PaperArticle

A New Symbolic Time Series Analysis Method Based on Time-to-Space Mapping, through a Symmetric Magnetic Field, Quantized by Prime Numbers

by Yiannis Contoyiannis, Pericles Papadopoulos, Niki-Lina Matiadou and Stelios M. Potirakis

Symmetry 2022, 14(11), 2366; https://doi.org/10.3390/sym14112366 - 09 Nov 2022

Cited by 2 | Viewed by 1202

Abstract

This work presents a new analysis method for two-symbol symbolic time series based on the time-to-space mapping achieved through a device of current carrying circular rings. An algorithm based on the theory of prime numbers is proposed for the approximate estimation of the [...] Read more.

This work presents a new analysis method for two-symbol symbolic time series based on the time-to-space mapping achieved through a device of current carrying circular rings. An algorithm based on the theory of prime numbers is proposed for the approximate estimation of the stratified magnetic field produced by the aforementioned device. The main property of the specific algorithm is that it quantizes the stratified magnetic field. If a two-symbol symbolic time series is used to determine the flow directions of the rings’ currents, a time-to-space mapping of the dynamics of the system producing the time series is observed. A unique “fingerprint” of the symbolic dynamics is shaped by the spatial allocation of the values of the six-valued symmetric quantized magnetic field produced by the device. This allows for the quantitative evaluation of the original system’s dynamics by analyzing the resultant quantized magnetic field values space allocation, in a spectrum ranging from the lack of dynamics (randomness) to the presence of dynamics at all scales (criticality). Two examples of application–corresponding to the extremes of the dynamics spectrum, specifically, for symbolic time series resulting from (a) a random numbers generator and (b) the spin alternation of 2D-Ising in its critical state, verify the reliable time-to-space mapping of the involved symbolic dynamics. Moreover, an application to the symbolic sequence produced by the DNA of the GAPDH (Glyceraldehyde-3-Phosphate Dehydrogenase) human gene is presented as a real-world, intermediate dynamics case. The proposed symbolic time series analysis method presents the advantage that can take into account information related to both symbols, which is particularly useful in analyzing two-symbol time series of relatively short length where the probabilities of occurrence of the two symbols are not equal. By inferring the universality class of an artificial-neural-network-based hybrid spin model through the value of the critical exponent

δ

, it is shown that for such time series, the proposed method provides a unique way to expose the real dynamics of the underlying complex system, in contrast to the analysis of waiting times in the time domain that leads to an ambiguous quantitative result. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos)

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25 pages, 3586 KiB

Open AccessArticle

OpenFOAM^TM Simulation of the Shock Wave Reflection in Unsteady Flow

by Lucas Monaldi, Luis Gutiérrez Marcantoni and Sergio Elaskar

Symmetry 2022, 14(10), 2048; https://doi.org/10.3390/sym14102048 - 01 Oct 2022

Cited by 1 | Viewed by 2030

Abstract

This work studies the impact of a shock wave traveling with non-constant velocity over straight surfaces, generating an unsteady and complex reflection process. Two types of shock waves generated by sudden energy released are studied: cylindrical and spherical. Several numerical tests were developed [...] Read more.

This work studies the impact of a shock wave traveling with non-constant velocity over straight surfaces, generating an unsteady and complex reflection process. Two types of shock waves generated by sudden energy released are studied: cylindrical and spherical. Several numerical tests were developed considering different distances between the shock wave origin and the reflecting surface. The Kurganov, Noelle, and Petrova (KNP) scheme implemented in the rhoCentralFoam solver of the OpenFOAM^TM software is used to reproduce the different shock wave reflections and their transitions. The numerical simulations of the reflected angle, Mach number of the shock wave, and position of the triple point are compared with pseudo-steady theory numerical and experimental studies. The numerical results show good accuracy for the reflected angle and minor differences for the Mach number. However, the triple point position is more difficult to predict. The KNP scheme in the form used in this work demonstrates the ability to capture the phenomena involved in the unsteady reflections. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos)

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18 pages, 4733 KiB

Open AccessArticle

Critical Dynamics in Stratospheric Potential Energy Variations Prior to Significant (M > 6.7) Earthquakes

by Dimitrios Z. Politis, Stelios M. Potirakis, Subrata Kundu, Swati Chowdhury, Sudipta Sasmal and Masashi Hayakawa

Symmetry 2022, 14(9), 1939; https://doi.org/10.3390/sym14091939 - 18 Sep 2022

Cited by 9 | Viewed by 1450

Abstract

Lithosphere–atmosphere–ionosphere coupling (LAIC) is studied through various physical or chemical quantities, obtained from different sources, which are observables of the involved complex processes. LAIC has been proposed to be achieved through three major channels: the chemical, the acoustic, and the electromagnetic. Accumulated evidence [...] Read more.

Lithosphere–atmosphere–ionosphere coupling (LAIC) is studied through various physical or chemical quantities, obtained from different sources, which are observables of the involved complex processes. LAIC has been proposed to be achieved through three major channels: the chemical, the acoustic, and the electromagnetic. Accumulated evidence supporting the acoustic channel hypothesis has been published, while atmospheric gravity waves (AGWs) play a key role in LAIC as the leading mechanism for the transmission of energy from the lower atmosphere to the stratosphere and mesosphere, associated with atmospheric disturbances observed prior to strong earthquakes (EQs). The seismogenic AGW is the result of temperature disturbances, usually studied through stratospheric potential energy (E_P). In this work, we examined 11 cases of significant EQs (M > 6.7) that occurred during the last 10 years at different geographic areas by analyzing the temperature profile at the wider location of each one of the examined EQs. The “Sounding of the Atmosphere using Broadband Emission Radiometry” (SABER) instrument, part of the “Thermosphere Ionosphere Mesosphere Energetics Dynamics” (TIMED) satellite, data were employed to compute the potential energy (E_P) of the AGW. Using the temperature profile, we first calculated E_P and determined the altitudes’ range for which prominent pre-seismic disturbances were observed. Subsequently, the E_P time series at specific altitudes, within the determined “disturbed” range, were for the first time analyzed using the criticality analysis method termed the “natural time” (NT) method in order to find any evidence of an approach to a critical state (during a phase transition from a symmetric phase to a low symmetry phase) prior to the EQ occurrence. Our results show criticality indications in the fluctuation of E_P a few days (1 to 15 days) prior to the examined EQs, except from one case. In our study, we also examined all of the temperature-related extreme phenomena that have occurred near the examined geographic areas, in order to take into account any possible non-seismic influence on the obtained results. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos)

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22 pages, 803 KiB

Open AccessArticle

Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument

by Marat Akhmet, Madina Tleubergenova, Roza Seilova and Zakhira Nugayeva

Symmetry 2022, 14(9), 1754; https://doi.org/10.3390/sym14091754 - 23 Aug 2022

Cited by 5 | Viewed by 1185

Abstract

In the paper, shunting inhibitory cellular neural networks with impulses and the generalized piecewise constant argument are under discussion. The main modeling novelty is that the impulsive part of the systems is symmetrical to the differential part. Moreover, the model depends not only [...] Read more.

In the paper, shunting inhibitory cellular neural networks with impulses and the generalized piecewise constant argument are under discussion. The main modeling novelty is that the impulsive part of the systems is symmetrical to the differential part. Moreover, the model depends not only on the continuous time, but also the generalized piecewise constant argument. The process is subdued to Poisson stable inputs, which cause the new type of recurrent signals. The method of included intervals, recently introduced approach of recurrent motions checking, is effectively utilized. The existence and asymptotic properties of the unique Poisson stable motion are investigated. Simulation examples for results are provided. Finally, comparing impulsive shunting inhibitory cellular neural networks with former neural network models, we discuss the significance of the components of our model. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos)

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34 pages, 2380 KiB

Open AccessArticle

Algebraic Theory of Patterns as Generalized Symmetries

by Adam Rupe and James P. Crutchfield

Symmetry 2022, 14(8), 1636; https://doi.org/10.3390/sym14081636 - 09 Aug 2022

Cited by 2 | Viewed by 1709

Abstract

We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence. For topological patterns in fully-discrete one-dimensional systems, future equivalence uniquely specifies a minimal semiautomaton. We demonstrate how the latter [...] Read more.

We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence. For topological patterns in fully-discrete one-dimensional systems, future equivalence uniquely specifies a minimal semiautomaton. We demonstrate how the latter and its semigroup algebra generalizes translation symmetry to partial and hidden symmetries. This generalization is not as straightforward as previously considered. Here, though, we clarify the underlying challenges. A stochastic form of future equivalence, known as predictive equivalence, captures distinct statistical patterns supported on topological patterns. Finally, we show how local versions of future equivalence can be used to capture patterns in spacetime. As common when moving to higher dimensions, there is not a unique local approach, and we detail two local representations that capture different aspects of spacetime patterns. A previously developed local spacetime variant of future equivalence captures patterns as generalized symmetries in higher dimensions, but we show that this representation is not a faithful generator of its spacetime patterns. This motivates us to introduce a local representation that is a faithful generator, but we demonstrate that it no longer captures generalized spacetime symmetries. Taken altogether, building on future equivalence, the theory defines and quantifies patterns present in a wide range of classical field theories. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos)

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15 pages, 1361 KiB

Open AccessArticle

Dynamics of Shunting Inhibitory Cellular Neural Networks with Variable Two-Component Passive Decay Rates and Poisson Stable Inputs

by Marat Akhmet, Madina Tleubergenova and Akylbek Zhamanshin

Symmetry 2022, 14(6), 1162; https://doi.org/10.3390/sym14061162 - 05 Jun 2022

Cited by 9 | Viewed by 1306

Abstract

Shunting inhibitory cellular neural networks with continuous time-varying rates and inputs are the focus of this research. A new model is considered with compartmental passive decay rates which consist of periodic and Poisson stable components. The first component guarantees the Poisson stability of [...] Read more.

Shunting inhibitory cellular neural networks with continuous time-varying rates and inputs are the focus of this research. A new model is considered with compartmental passive decay rates which consist of periodic and Poisson stable components. The first component guarantees the Poisson stability of the dynamics, and the second one causes irregular oscillations. The inputs are Poisson stable to take into account the more sophisticated environment of the networks. The rates and inputs are synchronized to obtain Poisson stable outputs. A new efficient technique for checking the recurrence, the method of included intervals, is applied. Sufficient conditions for the existence of a Poisson stable solution and its asymptotic stability were obtained. Numerical simulations of Poisson stable outputs as well as inputs are provided. Examples of the model with Poisson stable rates, inputs and outputs confirm the feasibility of theoretical results. Discussions were undertaken to provide additional light on the relation of the obtained results with practical and theoretical potentials of neuroscience. Quantitative characteristics are suggested, which can be useful for the future applications of the results. In particular, the center of antisymmetry for the degree of periodicity is determined. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos)

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23 pages, 8508 KiB

Open AccessArticle

A New 4D Hyperchaotic System with Dynamics Analysis, Synchronization, and Application to Image Encryption

by Tsafack Nestor, Akram Belazi, Bassem Abd-El-Atty, Md Nazish Aslam, Christos Volos, Nkapkop Jean De Dieu and Ahmed A. Abd El-Latif

Symmetry 2022, 14(2), 424; https://doi.org/10.3390/sym14020424 - 21 Feb 2022

Cited by 29 | Viewed by 2423

Abstract

In this paper, a new 4D hyperchaotic nonlinear dynamical system with two positive Lyapunov exponents is presented. Exhaustive dynamic analyses of the novel hyperchaotic model using several dynamical studies are described. The dynamics of the system considered are first investigated analytically and numerically [...] Read more.

In this paper, a new 4D hyperchaotic nonlinear dynamical system with two positive Lyapunov exponents is presented. Exhaustive dynamic analyses of the novel hyperchaotic model using several dynamical studies are described. The dynamics of the system considered are first investigated analytically and numerically to explore phenomena and the selection of hyperchaotic behavior utilized for designing image cryptosystem. Since the proposed hyperchaotic model has rich dynamics, it displays hidden attractors. It emerges from this dynamic the existence of a single unstable equilibrium point giving rise to self-excited attractors, hysteresis phenomenon, and hyperchaotic behavior strongly recommended for securing information by its character. Furthermore, the feasibility and synchronization of the proposed system are also presented by developing, respectively, Raspberry surveys and an adaptive synchronization approach of two identical hyperchaotic systems. By employing the hyperchaotic behavior of the 4D map, an image encryption scheme is proposed as well. It is one round of a pixel-based permutation and a bit-wise diffusion phase. The secret key of the 4D map is derived from the SHA-256 value of the input image. It acts as the signature of the input image. Hence, the secret key exhibits high sensitivity to single-bit alteration in the image, which makes the cryptosystem robust against chosen/known-plaintext attacks. Performance analyses prove that the proposed cryptosystem provides the best in terms of the performance/complexity trade-off, as compared to some recently published algorithms. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos)

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13 pages, 3902 KiB

Open AccessArticle

Compressive Strength Characteristics of Long Tubular Bones after Hyperthermal Ablation

by Denis Pakhmurin, Viktoriya Pakhmurina, Alexander Kashin, Alexey Kulkov, Igor Khlusov, Evgeny Kostyuchenko, Ivan Sidorov and Ilya Anisenya

Symmetry 2022, 14(2), 303; https://doi.org/10.3390/sym14020303 - 02 Feb 2022

Cited by 4 | Viewed by 1504

Abstract

Thermoablation is used in the treatment of tumorous bones. However, little is known about the influence such thermal treatment has on the mechanical properties of bone tissue. The purpose of this work was to study the influence of thermal treatment in a range [...] Read more.

Thermoablation is used in the treatment of tumorous bones. However, little is known about the influence such thermal treatment has on the mechanical properties of bone tissue. The purpose of this work was to study the influence of thermal treatment in a range of 60–100 °C (in increments of 10 °C) on the structural properties of pig femurs using an original approach that involved a periosteal arrangement of heating elements providing gradual dry heating of the bone from its periphery to its center. Heating of freshly extracted bone tissue segments was performed ex vivo using surface heaters of a Phoenix-2 local hyperthermia hardware system. Mechanical testing followed the single-axis compression scheme (traverse velocity of 1 mm/min). In the 60–90 °C range of heating, no attributes of reduced structural characteristics were found in the samples subjected to thermoablation in comparison to the control samples taken from symmetric areas of adjacent cylinders of healthy bones and not subjected to heat treatment. The following statistically significant changes were found as a result of compressing the samples to 100 °C after the heat treatment: reduced modulus of elasticity and increased elastic strain (strain-to-failure), mainly due to increases in plastic deformation. This finding may serve as evidence of a critical ex vivo change in the biomechanical behavior of bone tissues at such temperatures. Thus, ex vivo treatment of bone tissue in the thermal range of 60–90 °C may be used in studies of thermoablation efficiency against tumor involvement of bones. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics and Chaos)

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