A Numerical Analysis of the Structure of Periodic Orbits in Autonomous Functional Differential Equations

Abstract

Understanding the structure of periodic solutions in nonlinear, autonomous functional differential equations is a problem that often arises when such equations are used in the mathematical modeling of “real-world” phenomena. Knowledge of the existence, stability, and parameter dependence of such periodic solutions provides valuable insight into the general dynamics of the system. Stable steady states and periodic orbits are of particular interest since they correspond to observable states in the system being modeled. However, unstable steady states and periodic orbits are of importance as well since (through variation of parameters in the model) these solutions can themselves change stability and therefore, become “observable”.