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Entropy
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Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives
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Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Complexity".

Deadline for manuscript submissions: closed (29 February 2020) | Viewed by 7708

Special Issue Editors

Dr. Jiri Petrzela

E-Mail Website
Guest Editor
Department of Radio Electronics, FEEC, Brno University of Technology, Technicka 12, 616 00 Brno, Czech Republic
Interests: analog circuits; computer-aided analysis; chaos theory; nonlinear dynamics; numerical methods
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Milan Stork

E-Mail Website
Guest Editor
Department of Applied Electronics and Telecommunications, West Bohemia university, 30614 Pilsen, Czech Republic
Interests: analog circuit; digital circuit; chaotic systems; medical exercise systems; power systems; signal
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Many engineering, medical, environmental, economic, social, and other observable phenomena exhibit time evolution and can be successfully modeled via suitable mathematical expression; usually in the form of a set of differential equations. Because input–output relations between system quantities are generally non-proportional, associated dynamical behavior could be very complex or, under specific conditions, chaotic. Detection, description, analysis, quantification, and control of this random-like erratic motion associated with nonlinear dynamical systems is important due to universality (through dimensionless-less mathematical modeling) and several unique properties (sensitivity to initial conditions, mixing, dense attractors, fractal dimension, long-term unpredictability, continuous frequency spectrum, etc.).

Besides application in information theory, entropy is a general measure, commonly used for qualitative analysis of complex systems. Similar to Lyapunov exponents or fractal dimensions, entropy describes the complexity of dynamics with respect to system parameters, external forcing, initial conditions, or time instance.

Considering the recent advances reached in the field of chaotic systems (discovery of hidden attractors, multistability, different equilibrium structures, quasi-chaotic states, etc.) this Special Issue will collect new ideas and describe promising methods arising from the field of analysis and modeling of complex nonlinear dynamical systems.

This Special Issue will accept unpublished original papers and comprehensive reviews focused (but not restricted) on the following research areas:

  • Mathematical modeling of nature phenomena, artificial systems, and engineering problems
  • Analysis of nonlinear dynamical systems with complex behavior
  • New chaotic systems with special properties; both autonomous and driven
  • Experimental investigation of nonlinear lumped networks and circuits with spread parameters
  • Design of chaotic oscillators; described by both integer- and fractional-order
  • Investigation of electronic systems from the viewpoint of chaos evolution
  • Computer-aided quantification of continuous- and discrete-time dynamical flows
  • Advanced computational algorithms applied in real problems
  • Novel numerical methods dedicated to the qualitative analysis of dynamical flows
  • Algorithms for analysis of time sequences and entropy calculation

Dr. Jiri Petrzela
Prof. Dr. Milan Stork
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Complex systems
  • Dynamical systems
  • Entropy
  • Flow quantification
  • Chaos
  • Chaotic oscillators
  • Nonlinear circuits
  • Numerical algorithms
  • Strange attractors

Published Papers (3 papers)

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Research

20 pages, 3404 KiB  
Article
Higher-Order Hamiltonian for Circuits with (α,β) Elements
by Zdeněk Biolek, Dalibor Biolek, Viera Biolková and Zdeněk Kolka
Entropy 2020, 22(4), 412; https://doi.org/10.3390/e22040412 - 05 Apr 2020
Cited by 2 | Viewed by 2141
Abstract
The paper studies the construction of the Hamiltonian for circuits built from the (α,β) elements of Chua’s periodic table. It starts from the Lagrange function, whose existence is limited to Σ-circuits, i.e., circuits built exclusively from elements located on [...] Read more.
The paper studies the construction of the Hamiltonian for circuits built from the (α,β) elements of Chua’s periodic table. It starts from the Lagrange function, whose existence is limited to Σ-circuits, i.e., circuits built exclusively from elements located on a common Σ-diagonal of the table. We show that the Hamiltonian can also be constructed via the generalized Tellegen’s theorem. According to the ideas of predictive modeling, the resulting Hamiltonian is made up exclusively of the constitutive relations of the elements in the circuit. Within the frame of Ostrogradsky’s formalism, the simulation scheme of Σ-circuits is designed and examined with the example of a nonlinear Pais–Uhlenbeck oscillator. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives)
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35 pages, 9853 KiB  
Article
On the Entropy of Events under Eventually Global Inflated or Deflated Probability Constraints. Application to the Supervision of Epidemic Models under Vaccination Controls
by Manuel De la Sen, Asier Ibeas and Raul Nistal
Entropy 2020, 22(3), 284; https://doi.org/10.3390/e22030284 - 29 Feb 2020
Cited by 4 | Viewed by 1924
Abstract
This paper extends the formulation of the Shannon entropy under probabilistic uncertainties which are basically established in terms or relative errors related to the theoretical nominal set of events. Those uncertainties can eventually translate into globally inflated or deflated probabilistic constraints. In the [...] Read more.
This paper extends the formulation of the Shannon entropy under probabilistic uncertainties which are basically established in terms or relative errors related to the theoretical nominal set of events. Those uncertainties can eventually translate into globally inflated or deflated probabilistic constraints. In the first case, the global probability of all the events exceeds unity while in the second one lies below unity. A simple interpretation is that the whole set of events losses completeness and that some events of negative probability might be incorporated to keep the completeness of an extended set of events. The proposed formalism is flexible enough to evaluate the need to introduce compensatory probability events or not depending on each particular application. In particular, such a design flexibility is emphasized through an application which is given related to epidemic models under vaccination and treatment controls. Switching rules are proposed to choose through time the active model, among a predefined set of models organized in a parallel structure, which better describes the registered epidemic evolution data. The supervisory monitoring is performed in the sense that the tested accumulated entropy of the absolute error of the model versus the observed data is minimized at each supervision time-interval occurring in-between each two consecutive switching time instants. The active model generates the (vaccination/treatment) controls to be injected to the monitored population. In this application, it is not proposed to introduce a compensatory event to complete the global probability to unity but instead, the estimated probabilities are re-adjusted to design the control gains. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives)
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19 pages, 2830 KiB  
Article
Lagrangian for Circuits with Higher-Order Elements
by Zdenek Biolek, Dalibor Biolek and Viera Biolkova
Entropy 2019, 21(11), 1059; https://doi.org/10.3390/e21111059 - 29 Oct 2019
Cited by 6 | Viewed by 2861
Abstract
The necessary and sufficient conditions of the validity of Hamilton’s variational principle for circuits consisting of (α,β) elements from Chua’s periodical table are derived. It is shown that the principle holds if and only if all the circuit elements [...] Read more.
The necessary and sufficient conditions of the validity of Hamilton’s variational principle for circuits consisting of (α,β) elements from Chua’s periodical table are derived. It is shown that the principle holds if and only if all the circuit elements lie on the so-called Σ-diagonal with a constant sum of the indices α and β. In this case, the Lagrangian is the sum of the state functions of the elements of the L or +R types minus the sum of the state functions of the elements of the C or −R types. The equations of motion generated by this Lagrangian are always of even-order. If all the elements are linear, the equations of motion contain only even-order derivatives of the independent variable. Conclusions are illustrated on an example of the synthesis of the Pais–Uhlenbeck oscillator via the elements from Chua’s table. Full article
(This article belongs to the Special Issue Nonlinear Dynamics and Entropy of Complex Systems: Advances and Perspectives)
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