Aims and scope

The main objective of Discrete Dynamics in Nature and Society (DDNS) is to foster links between basic and applied research relating to discrete dynamics of complex systems encountered in the natural and social sciences.

Discrete dynamics reflects a new emerging tendency towards utilization of iterative mathematical models—systems of difference equations—to describe the behavior of complex systems. It has became clear from the latest development in discrete modeling that such models have a simpler structure and provide many more possibilities for generating and describing complex non-linear phenomena, including chaotic regimes and fractals.

However, further developments in such a discrete mathematical approach are restricted by the absence of general principles that could play the same role as the variational principles in physics. Discrete Dynamics in Nature and Society aims to elaborate such principles, which are expected to lead to a better understanding of the exact meaning of “discrete” time and space, and, to the creation of a new “calculus” for discrete complex dynamics. These general principles should provide direct construction of difference equations for their further use in mathematical modeling of complex, living and thinking systems as it was happened in classical mechanics for the inert matter.

The journal intends to stimulate publications directed to the analyses of computer generated solutions and chaotic in particular, correctness of numerical procedures, chaos synchronization and control, discrete optimization methods among other related topics.

The journal will provide a channel of communication between scientists and practitioners working in the field of complex systems analysis and will stimulate the development and use of discrete dynamical approach.

Discrete Dynamics in Nature and Society will publish original, high-quality, research papers. In addition there will be regular editorials, invited reviews, a letters section and a news section containing information on future events, and book reviews.

Special Issue on Chaos and Synchronization in Discrete Systems
Submission Date: 2025-02-21

Description

Discrete dynamical systems are shown to have useful applications in many disciplines such as science, engineering, and economy. Recently, some mathematical models that are governed by difference equations have been developed to study the dynamics of some epidemiological diseases, economic games, population growth, etc. The discrete-time systems are also helpful to approximate the solutions of the corresponding nonlinear fractional order systems that do not have analytic solutions, in terms of a finite representation of elementary functions.

The discrete dynamical systems display various complex dynamics such as Neimark-Sacker bifurcation, flip bifurcation, fold bifurcation, strange attractors, hidden attractors, and multi-attractors coexistence. In addition, chaotic attractors have recently been found in nonlinear discrete dynamical systems. Therefore, chaos synchronization and chaos control in discrete dynamical systems have become two focal points of research interest. Indeed, there are some practical situations where the system’s irregular and unpredictable dynamics should be eliminated and stabilized to a specific steady state, which is meant by chaos control. Recently, some useful schemes have been proposed to control the discrete dynamical system to its equilibrium state such as hybrid control feedback and OGY schemes. On the other hand, chaos synchronization between two chaotic dynamical systems implies that the two systems display identical behaviors and the existence of a strong correlation between them. In addition, there exist several methods to achieve synchronization in chaotic discrete dynamical systems such as the projective synchronization method and the complete synchronization method which is based on the contraction mapping theorem. Furthermore, synchronization on networked discrete dynamical systems with impulsive couplings can be achieved. Thus, when a discrete-time dynamical system is chaotic and how to control and synchronize such system have been three particularly important problems.

The focus of this Special Issue is to investigate chaotic behavior, control, and synchronization phenomena in discrete dynamical systems, with applications ranging from cryptography to secure communication protocols. New techniques for quantifying the chaotic dynamics in discrete dynamical systems will be presented. Elegant techniques for investigating the bifurcation phenomena in such systems will be explained. In addition, new schemes for achieving chaos control and chaos synchronization in discrete dynamical systems will be introduced. Moreover, new applications of discrete dynamical systems to science and technology will be presented such as applications of discrete dynamical systems to cryptography and secure communication protocols, discrete dynamical models on networked systems, discretization of fractional-order models, discrete-time models in mathematical biology, and game theory.

Potential topics include but are not limited to the following:

    Chaos in discrete dynamical systems
    Chaotic, hyperchaotic maps and Marotto’s chaos
    Synchronization in chaotic discrete dynamical systems
    Chaos control in discrete dynamical systems
    Hidden attractors in discrete dynamical systems
    Dynamics of discrete models in biology, physics, chemistry and engineering
    Dynamics of discrete models in economy and dynamic games
    Discrete epidemic model and population dynamics
    Bifurcation phenomena in discrete dynamical systems and normal forms
    Complexity and entropy in discrete dynamical systems
    Discretized fractional-order dynamical systems
    Chaotic systems governed by Grunwald-Letnikov fractional derivative
    Applications of discrete dynamical systems to cryptography and secure communication protocols
    Discrete dynamics on networked systems

Editors

Lead Editor

Ahmed Ezzat Matouk1
1Majmaah University, Al Majma'ah, Saudi Arabia