A dynamical system is a mathematical model that describes how a system changes over time. It is composed of a set of variables and equations that govern the behavior of the system.
Illustration is used in dynamical systems to visually represent the behavior and patterns of the system. It can help to better understand complex equations and make predictions about the future behavior of the system.
There are various types of illustrations used in dynamical systems, including phase portraits, bifurcation diagrams, and time series plots. Each type of illustration provides a different perspective on the behavior of the system.
Dynamical systems are useful in science as they allow scientists to model and predict the behavior of complex systems, such as weather patterns, population dynamics, and chemical reactions. They also help to understand the underlying mechanisms that drive these systems.
Dynamical systems have a wide range of real-world applications, including in physics, biology, economics, and engineering. They are used to study and predict the behavior of natural and man-made systems, such as climate change, disease spread, financial markets, and traffic flow.