Advances in Nonlinear Analysis: Theory, Methods and Applications

Dear Colleagues,

The dynamics of many social and natural systems are nonlinear. Such nonlinear model systems require the application of methods from nonlinear dynamics, chaos theory and the theory of stochastic processes. Depending on the nature of the system, they may exhibit a variety of properties and interact in different ways. In recent years, these nonlinear model systems have undergone rapid development because they allow us to adequately describe processes in various natural and social systems. Mathematical modelling provides such an opportunity and generates testable forecasts. It also provides a means to design and evaluate protocols, enabling management and control. Agent-based models have seen significant development in recent years, as they offer a means of describing processes in complex systems effectively. When the number of agents is small and chaos in their behavior is limited, it is possible to describe the system of interacting agents with relatively simple systems of ordinary or partial differential equations. Consequently, deterministic modelling using various types of differential equations is a widely used method. There are different methods for solving these systems of equations. Some yield values of the solution corresponding to specified time and space coordinates. However, in some cases, the solution itself, derived under appropriate assumptions about its nature, can provide valuable insights.

The aim of this Special Issue is to explore the nonlinear properties of natural and social systems, utilizing appropriately developed deterministic and stochastic models while employing methods from nonlinear dynamics, chaos theory and stochastic modelling. Additionally, qualitative modelling systems should be investigated, and modern analytical and numerical mathematical methods should be applied to obtain new solutions for such systems.

Dr. Ivan P. Jordanov
Guest Editor

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