Algorithm for the numerical proof of the existence of periodic trajectories in two-dimensional nonautonomous systems of ordinary differential equations

Abstract

We suggest an algorithm that permits one to prove the existence of limit periodic trajectories (cycles) in two-dimensional nonautonomous dissipative systems with periodic coefficients with the use of computational methods alone. We prove a fixed point theorem for two-dimensional mappings and describe methods of its application to two-dimensional nonautonomous systems with the use of the Poincare mapping and interval arithmetics.