Discrete systems have been a topic of investigation in many branches of science. Physical models involving natural or artificial agents are increasingly used to describe properties of the dynamics of discrete oscillators, propagation of specific characteristics in discrete systems, and even spread of infectious diseases. To study such systems, a wide range of novel mathematical methods have been implemented and improved. Novel new simulation tools are developed in many ways. The mathematical apparatus that supports the analysis of various methodologies has witnessed a tremendous increase in applications to improve the quality of human lives.

Many challenges arise in the investigation of discrete systems. Firstly, the determination of conditions under which those systems possess desirable solutions is an open area of opportunity in mathematics. Furthermore, computational approximations of such systems require a thorough analysis of the reliability of the numerical models developed. The development of mathematical tools to investigate stability and convergence has been crucial for guaranteeing real-life results in the natural world. Finally, the implementation and analysis of new and trust-worthy approaches in artificial intelligence is another important avenue of research to obtain real-time results of complex model systems.

The aim of this Special Issue is to provide an opportunity for researchers to report on their latest achievements in this area. Determinations of qualitative features of the solutions of these systems and their simulation techniques are of special interest. Papers that study the existence of solutions and properties of the solution spaces are welcome. The latest results emphasizing rigorous analyses for simulating the dynamics of complex models in the natural sciences and engineering are solicited for this issue. Insights into cross-fertilization of machine learning in complex system modelling strategies are also of interest. Both deterministic and non-deterministic models will be considered. Pertinent applications for solving practical problems are encouraged. Both original research and review articles are welcome.

Potential topics include but are not limited to the following:

• Discrete nonlinear systems and simulation techniques
• Integer- and fractional-order systems and equations
• Existence and uniqueness of relevant solutions
• Uncertain systems
• Approximation theory
• Discrete methods for the simulation of nonlinear models (finite differences, finite elements, finite volumes, quadrature methods, etc.)
• Structure-preserving algorithms
• Efficiency, accuracy, stability, and convergence analyses
• Multi-physical applications
• Techniques for data-driven models
• Developments and analysis of machine learning and deep machine learning