Dynamics characterizes the phenomena we encounter in both inanimate and animate systems, including social systems. It refers to the time evolution of key features of these processes. In most complex problems, dynamics cannot be overlooked; it is essential for gaining insights and achieving meaningful results. A useful framework for analyzing dynamics is the concept of a dynamic system, defined by input (control), state, and output spaces, along with a state transition equation. By starting from an initial state, we can derive a sequence of states (outputs) based on consecutive inputs (controls), resulting in a trajectory. State transition equations can take various forms, such as differential or difference equations, and can be linear or nonlinear, deterministic or stochastic, or even fuzzy. These characteristics may lead to challenges for analysts, including numerical difficulties, instability, or chaotic behavior. This volume explores modern tools and techniques for modeling dynamics, focusing on two critical areas: automation and robotics, and biological systems. Additionally, it presents new applications that can benefit from effective modeling tools, including examples from security systems.
