Estimates of Periods and Global Continua of Periodic Solutions for State-Dependent Delay Equations

Abstract

We study the global Hopf bifurcation of periodic solutions for one-parameter systems of state-dependent delay differential equations, and specifically we obtain a priori estimates of the periods in terms of certain values of the state-dependent delay along continua of periodic solutions in the Fuller space $C(\mathbb{R};\mathbb{R}^{N+1})\times\mathbb{R}^2$. We present an example of three-dimensional state-dependent delay differential equations to illustrate the general results.