Such models utilise differential equations and discrete-time maps to simulate phenomena ranging from the oscillatory behaviour of populations to complex bifurcation events, where small changes in ...

Ordinary differential equations (ODEs) and difference equations serve as complementary tools in the mathematical modelling of processes evolving in continuous and discrete time respectively.

This study explores a method for discovering governing equations from data using sparse identification of nonlinear dynamical systems.

How great an effect does self-generated spatial structure have on logistic population growth? Results are described from an individual-based model (IBM) with spatially localized dispersal and ...

APPM 5460 Methods in Applied Mathematics: Dynamical Systems and Differential Equations Introduces the theory and applications of dynamical systems through solutions to differential equations.Covers ...

When searching for highly complicated dynamics, however, the Conley index may also become highly complicated, and difficult to interpret. I will present an automated approach to processing Conley ...