A discrete dynamical system is a mathematical model that describes the evolution of a system over time in a step-by-step manner. It is used to study the behavior and properties of systems that change or evolve in a discontinuous or discrete fashion. In a discrete dynamical system, time is represented by a sequence of discrete moments or steps, rather than as a continuous flow. The state of the system at each time step is determined by its previous state and some predefined rules or equations. These rules dictate how the system evolves from one state to another. The state of the system can be represented by a set of variables or parameters, which can have different values at each time step. The dynamics of the system are determined by the interactions between these variables and how they change over time. Discrete dynamical systems can be found in various fields such as physics, biology, economics, computer science, and engineering. They are often used to model phenomena where small changes or events occur at specific intervals, rather than continuously. One common example of a discrete dynamical system is the logistic map, which models population growth. The population size at each time step depends on its previous size according to a specific equation. This model helps understand how population dynamics can exhibit stability, periodicity, or chaos depending on certain parameters. Another example is cellular automata, which simulate complex patterns and behaviors based on simple rules applied to individual cells arranged in a grid. These systems have been used to study various phenomena such as traffic flow, pattern formation, and social dynamics. Overall, discrete dynamical systems provide valuable insights into complex systems by studying their behavior through discrete steps instead of continuous changes over time. They help analyze stability, periodicity, attractors, bifurcations, chaos theory, and other dynamic properties within various scientific disciplines. # References ```dataview Table title as Title, authors as Authors where contains(subject, "dynamical system") or contains(subject, "Dynamical system") or contains(subject, "Dynamical System") ```