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 Intelligent Systems for Discrete Modelling of IoT Networks in Safety Critical Systems
Submission Date: 2026-07-31

Description

In recent years, the world has witnessed an unprecedented expansion of Internet of Things (IoT) networks and connected devices. Millions of sensors, actuators, and smart gateways are now continuously monitoring, transmitting, and exchanging information across industrial, urban, healthcare, and social environments.

The exponential increase in the amount of information being generated and transferred across these networks introduces significant challenges related to scalability, latency, energy consumption, and data integrity. In complex infrastructures, data are often incomplete, delayed, or corrupted, while network topologies evolve dynamically. These features call for new discrete-time and network-based models capable of capturing stochasticity, communication constraints, and hybrid dynamics between cyber and physical components.

A particularly critical trend is the deployment of IoT devices in critical systems, such as power grids, transportation systems, water distribution systems or healthcare infrastructures among others. In such domains, even minor disturbances or component failures can propagate rapidly through interconnected subsystems. As a result, malfunctions or cyberattacks targeting these networks can trigger severe socioeconomic, environmental, or health-related consequences, including large-scale service disruptions, safety hazards and so on. Ensuring reliable operation under such conditions requires modelling and control approaches that explicitly account for stringent safety constraints.

Consequently, the security, reliability, and resilience of IoT-enabled safety-critical systems have become central research priorities. Beyond traditional cybersecurity concerns, these systems demand verifiable, explainable, and robust decision-making mechanisms. Formal methods, verification techniques, and interpretable models play a key role in providing guarantees on system behavior. In parallel, growing attention is being paid to adversarial robustness, attack-resilient learning, and secure-by-design control frameworks capable of withstanding both accidental faults and intentional cyberattacks.

At the same time, advances in artificial intelligence, particularly machine learning, have enabled powerful data-driven modelling and control solutions. However, in safety-critical settings, purely data-driven approaches are often insufficient due to their limited interpretability and lack of formal guarantees. In this context, hybrid intelligence, combining discrete and hybrid system models, data-driven learning, and domain knowledge, emerges as a promising paradigm. Relevant contributions include human-in-the-loop (HITL) approach, adaptive and cooperative control frameworks, and architectures in which learning components operate under formal supervision.

For these reasons, this special issue focuses on bridging discrete modelling formalisms with intelligent, secure, and resilient decision-making for critical systems. Rather than addressing IoT or artificial intelligence in isolation, the emphasis is placed on discrete-time and event-driven models as the foundational layer for integrating learning, control, and cybersecurity mechanisms. This perspective supports solutions that are robust, interpretable, and verifiable, while remaining applicable to real-world critical infrastructures.

The special issue welcomes contributions covering theoretical developments of specific discrete and hybrid modelling solutions, the application of existing intelligent and security techniques, and the proposal of new algorithms and hybrid modelling approaches. However, particular emphasis is placed on application papers demonstrating the deployment and validation of these methods in real systems.

To promote scientific rigor and reproducibility, the special issue explicitly encourages submissions that provide open datasets, simulation environments, benchmarking tools, or reproducible experimental frameworks. Contributions enabling fair comparison, validation, and reuse of models and algorithms are particularly valued, as they support transparent and verifiable research outcomes.

The scope and objectives of this special issue are closely aligned with the aims of Discrete Dynamics in Nature and Society, contributing to advances in discrete and hybrid system modelling, systems engineering, automation, networked cyber-physical systems, and computational intelligence applied to complex real-world problems.

Potential topics include but are not limited to the following:

    Discrete-time and event-driven modeling of large-scale IoT and cyber-physical systems
    Hybrid models for critical systems
    Graph neural networks and graph signal processing for dynamic IoT topologies
    Cyber-resilience and fault-tolerant design for IoT-based critical infrastructures
    Secure and privacy-preserving data transmission and learning in distributed networks
    Resilient consensus and coordination under communication constraints or attacks
    Federated and edge learning for real-time IoT analytics and control
    Anomaly detection, fault diagnosis, and predictive maintenance of critical cyber-physical systems
    Robust and explainable AI for safety-critical control and decision-making
    Digital twins and hybrid simulation frameworks for IoT-enabled systems
    Integration of discrete dynamic models with reinforcement and adaptive learning methods
    Applications of ML-based discrete modeling in critical cyber-physical systems
    Benchmarking, datasets, and reproducible platforms for secure and intelligent IoT networks

Editors

Lead Guest Editor

Álvaro Michelena1
1Polytechnic School of Engineering of Ferrol, University of A Coruña, Spain

Guest Editors

Esteban Jove1 | Dragan Simic2 | Francisco Zayas-Gato3
1University of A Coruña, Spain
2University of Novi Sad , Serbia
3University of A Coruña, Spain

https://onlinelibrary.wiley.com/doi/toc/10.1155/3059.SI-2026-000034

Special Issue on Next-Generation Mathematical Solving: Applied Mathematics in Action
Submission Date: 2026-11-30

Description

Introduction

Mathematics is at the heart of innovation, powering solutions to some of the most complex challenges across science, engineering, and society. The Special Collection on “Next-Generation Mathematical Solving: Applied Mathematics in Action” invites contributions that showcase how advanced modelling, rigorous analysis, and solver design can transform real-world problem-solving. This initiative highlights research that goes beyond theory—delivering practical, measurable impact through mathematical reasoning and computation. We welcome interdisciplinary approaches, creative modelling strategies, and studies that demonstrate the power of applied mathematics in driving progress across diverse domains.

Scope and Objectives

This special collection invites contributions that represent the next generation of mathematical solving, integrating modelling, analysis, and solver design to address complex real-world problems. We aim to bring together studies that demonstrate how mathematical methods and solvers design can improve understanding, performance, and decision-making across disciplines.

We particularly welcome contributions from early-career researchers, interdisciplinary teams, and those proposing creative modelling approaches to complex systems. This collection highlights researchers and practitioners who use applied mathematics not only to describe systems, but to deliver concrete, measurable solutions.

Whether your work addresses engineering or industrial systems, biological processes, social dynamics, or solving frameworks with practical implications, we are interested in research showing how mathematics enables progress through rigorous reasoning and effective computation.

While data-driven and AI-based methods are relevant, the emphasis should remain on the mathematical formulation, analysis, and solver development, rather than purely empirical outcomes.

Potential topics include but are not limited to the following:

    Mathematical modelling and analysis of complex or dynamic systems
    Advances in optimization, simulation, and numerical computation
    Development and validation of efficient solvers and scalable algorithms
    Integration of mathematical and data-driven methodologies
    Uncertainty quantification, robustness, and sensitivity analysis
    Inverse problems and parameter estimation in mathematical models
    Numerical analysis and discretization techniques for complex systems
    Multi-objective and multi-scale modelling frameworks
    Methodological advances ensuring robustness and transparency in mathematical modelling
    Cross-disciplinary applications in logistics, engineering, biology, health, energy, or the environmental sciences.

Editors

Lead Guest Editor

Chunrui Zhang1
1Northeast Forestry University, China