DISCRETE DYNAMICAL SYSTEM Meaning and
Definition
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A discrete dynamical system refers to a mathematical concept that describes the evolution of a system over time in a step-by-step manner. It involves a set of distinct, separate states or values that the system can occupy at each step of the process. This system is defined by a set of rules or equations that govern the transition from one state to another.
In a discrete dynamical system, time is divided into discrete intervals or steps, with the system updating its state only at these specific points. At each interval, the system undergoes a transformation or change based on the current state and the defined rules. These rules can be deterministic, meaning that the outcome is completely determined by the initial state, or they can incorporate randomness, introducing a level of uncertainty into the system's evolution.
The term "dynamical" refers to the idea that the system is dynamic and can change over time. It emphasizes the continuous progression and transformation of the system's state across the defined time intervals. By analyzing the behavior of a discrete dynamical system, mathematicians can gain insights into various phenomena such as population dynamics, weather patterns, economic models, and biological processes.
Overall, a discrete dynamical system represents a mathematical framework used to model and understand the evolution of systems that exhibit discrete states and update their values according to specified rules at discrete points in time.
