Topic: Discontinuous Systems: Complex Dynamics and Optimal Control

Discontinuous differential systems are widely employed to model and analyze diverse dynamic processes across the real world, spanning fields such as ecological dynamics (e.g., predator–prey systems), epidemic transmission (e.g., dengue, avian influenza, dysentery), cancer progression, gene regulatory networks, engineering mechanics, electrical systems, automatic control, and economics. Influenced by impulse effects, time-varying delays, and stochastic disturbances, such systems often exhibit highly complex dynamical behaviors, including sliding modes, periodic oscillations, limit cycles, chaos, and bifurcations. In parallel, practical demands for stability and performance in control engineering motivate the design of various controllers—such as sliding mode and adaptive controllers—to achieve finite-, fixed-, and predefined-time stability and optimization for discontinuous systems. This special issue seeks to showcase recent advances in the analysis of complex dynamics and the development of time-constrained control and optimization methods for discontinuous systems, a topic of growing interdisciplinary interest.

Discontinuous systems, sliding mode dynamics, periodic oscillation, limit cycle, chaos, stability, bifurcation, optimal control