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 Discrete Optimization and Decision Making
Submission Date: 2024-12-27

Description

Optimization of discrete dynamics refers to the process of finding the best possible solution, or set of solutions, to a problem where the system evolves in discrete time steps. This type of optimization is particularly relevant in fields where the state of the system changes at specific intervals, such as in digital systems, financial markets, supply chain management, and various engineering applications. Discrete dynamics involves systems that evolve in distinct time steps rather than continuously, and these systems can be described by difference equations or discrete maps. Discrete dynamics play an important role in many areas, including digital control systems, economic models, population dynamics, and inventory systems. Optimization involves finding the best solution from a set of feasible solutions, typically by maximizing or minimizing an objective function, subject to certain constraints. With the increasing complexity of industrial problems and the need for efficient decision-making, harnessing the power of advanced algorithms and optimization techniques has become vital. Traditional methods often fall short when faced with multiple complex objectives that need to be considered simultaneously. This is where optimization methods can be used to revolutionize this process. Using artificial intelligence, machine learning, and mathematical modelling, engineers can optimize and control uncertain problems with more precision and efficiency. These optimization methods provide a systematic approach to analyze and optimize complex industrial problems, whether it is structural design, production processes, energy systems, or even autonomous vehicles.

The optimization of discrete dynamics involves the development and application of various mathematical and computational techniques to find the best solutions for systems that evolve in discrete time steps, addressing both theoretical and practical challenges. Current challenges include scalability and the development of algorithms that can efficiently handle large-scale discrete dynamic systems, ensuring that optimization solutions are robust and resilient to uncertainties and variations in system parameters, and implementing optimization algorithms that can operate in real-time for systems that require immediate decision-making. Also essential for navigating complex and dynamic decision-making problems are interdisciplinary approaches, combining techniques from different fields, such as machine learning and artificial intelligence (AI), to enhance the optimization of discrete dynamic systems, and the integration of emerging digital technologies with traditional optimization methods.

This Special Issue aims to bring together contributions that address the above challenges and contribute to advanced optimization techniques of discrete dynamics. We encourage submissions on linear and nonlinear programming, dynamic programming, and stochastic optimization. We welcome both original research and review articles.

Potential topics include but are not limited to the following:

    Optimal control models of fractional order systems
    Optimization algorithms for supply chain management
    Digital control systems
    Economic models
    Population dynamics
    Inventory systems
    Markov decision processes
    Stochastic programming
    Emerging digital technologies, such as blockchain, AI, or Internet of Things
    Optimal scheduling models
    Combinatorial optimization

Editors

Lead Editor

S Priyan1
1Amity University Tashkent, Uzbekistan

Guest Editors

Sathiyaraj Thambiayya1
1UCSI University, Kuala Lumpur, Malaysia

Special Issue on Mine Safety and Sustainable Resilience Energy System
Submission Date: 2024-12-27

Description

The development of green and sustainable energy is a significant challenge for the contemporary society, and effective risk management plays a crucial role in ensuring smooth progression of the entire process while minimising potential negative impacts. Through system science, decision analysis, and dynamic modeling, studying the dynamics of energy complex systems can enhance our understanding and prediction of energy system evolution. This can provide valuable insights for energy decision makers. However, in this process, there are various uncertain factors, and how to accurately establish a mathematical model to capture the dynamic evolution of the system is still a problem to be solved. Thus, it is possible to develop adaptable models and utilise multiscale modelling methods to capture both global and local system characteristics. This will facilitate the study of risk management and control in the energy system, providing scientific support to achieve green and sustainable energy development.

By focusing on experimental techniques, monitoring systems, mathematical models, and cutting-edge numerical methods, this special issue aims to catalyze scientific and technological innovation in energy sustainability and natural disaster prevention on a global scale. In addition, by effectively managing and controlling the risks associated with shifting from traditional energy to clean energy, including uncertainty and potential losses, and exploring risk management strategies for renewable energy technologies, we can ensure stable and sustainable business development. This also promotes the optimization of our energy structure.

This Special Issue aims to collect original research and review articles, elaborating on theories, research methods, and mathematical or empirical research related to occupational health, safety, and resilient energy systems. These articles are expected to provide theoretical and/or practical significance.

Potential topics include but are not limited to the following:

    Green and sustainable exploitation of fossil fuels
    Energy risk management and intelligent monitoring and early warning
    Energy storage and transportation risks and their resilience assessment
    Research on the Mechanism and Prevention of Dynamic Disasters in Deep Mines
    Assessment of Emergency Management Capability for Sudden Energy Accidents
    Decision dynamics of complex systems
    Artificial intelligence and big data for natural disaster prevention and control
    Assessment and prevention of occupational health damage in mines
    Emergency resource scheduling and assessment of emergency rescue capabilities
    Mine safety and emergency response

Editors

Lead Editor

Bin Gong1
1Brunel University London, China

Guest Editors

Yun QI1 | Jintao LU2 | Wei WANG3 | Jianhui Cong4
1Shanxi Datong University, Datong, China
2Taiyuan University of Science and Technology, Taiyuan, China
3Shanxi Datong University, Datong, China
4Shanxi University, Taiyuan, China

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