Hopf bifurcation of integro-differential equations

A method reducing integro-differential equations (IDEs) to system of ordinary ones is proposed. On this base stability and bifurcation phenomena in critical cases are studied. Analog of Hopf bifurcation for scalar IDEs of first order is obtained. Conditions of periodic solution existence are proposed. One of the conclusions is the following: phenomena characterized by two dimension systems of ODEs appear for scalar IDEs

Floquet Theory and Stability of Nonlinear Integro-differential Equations

One of the classical topics in the qualitative theory of differential equations is the Floquet theory. It provides a means to represent solutions and helps in particular for stability analysis. In this paper first we shall study Floquet theory for integro-differential equations (IDE), and then employ it to address stability problems for linear and nonlinear equations