dynamical

in differential equations, topology, and chaos theory. Differential Equations and Iterative Maps Nonlinear Differential Equations: Equations where derivatives depend on nonlinear functions of the variables, e.g., the Lorenz sy

\] where \( \mathbf{f} : \mathbb{R}^n \to \mathbb{R}^n \) is a vector-valued function defining the rules of change. Key considerations: Initial conditions: The starting state \( \mathbf{x}(t_0) \) is crucial for solving the syste