The existence of periodic solutions for coupled pantograph Rayleigh system

In this paper, we consider the existence of periodic solutions for coupled pantograph Rayleigh system, which is a special case of coupled delay Rayleigh system with unbounded memory. The mathematical model of this kind of coupled systems is first proposed. Also, based on a novel method combining coincidence degree theory with Lyapunov method and graph theory, an easily verifiable sufficient criterion is given. As illustrations, a simulation example is presented to show the effectiveness and feasibility of the proposed criterion.