Local Dynamics of a Chain of Coupled Van der Pol Equations

Abstract

We consider the problem of local dynamics of a system of a diffusive-coupled chain of the Van der Pol equations. A transition to the spatially distributed nonlinear boundary-value problem is performed on the assumption of a large number of elements in the chain. Critical cases in the problem of the equilibrium-state stability are emphasized, and all of them have infinite dimension. An algorithm for reducing the input problem to a study of special nonlinear equations of the parabolic type with one or two spatial variables is developed. The nonlocal dynamics of such equations determines the behavior of all solutions of the input problem in the neighborhood of the equilibrium state.