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In the paper, we are concerned with the existence of periodic solutions for a coupled Rayleigh system. By combining graph theory with coincidence degree theory as well as Lyapunov function method, two new sufficient conditions on the existence of periodic solutions for the coupled Rayleigh system are established. Our results on the existence of periodic solutions for the coupled Rayleigh system improve those obtained in the existing literature for coupled Rayleigh system. Hence, our results are new and complementary to the existing papers.First part title: IntroductionSecond part title: PreliminariesThird part title: The existence of periodic solutionsFourth part title: Numerical testFive part title: Conclusion

A graph-theoretic method to study the existence of periodic solutions for a coupled Rayleigh system via inequality techniques