Dynamical systems encompass mathematical models that describe how quantities change over time based on specific rules or equations. These systems explore the evolution of variables or states within a system as time progresses, investigating their behaviors, stability, and patterns. They encompass a broad range of fields, including physics, biology, economics, and engineering, allowing the study of complex phenomena such as weather patterns, population dynamics, chaotic behavior, and more. Understanding dynamical systems involves analyzing their behavior, attractors, bifurcations, and stability, offering insights into the underlying mechanisms governing complex dynamic processes and aiding in predictions, control, and optimization in various disciplines.