Periodic solutions of stochastic coupled systems on networks with periodic coefficients

• Periodic solutions of stochastic coupled systems on networks are considered.
• A systematic method of proving the existence of periodic solutions is provided.
• The methods used are graph theory and Lyapunov method.
• Numerical example is introduced to illustrate the results.

This paper is concerned with periodic solutions of periodic stochastic coupled systems on networks. A systematic method of proving the existence of periodic solutions to the general stochastic coupled systems on networks is provided by using combined method of graph theory and Lyapunov method. Moreover, sufficient conditions for the existence of the periodic solutions to a type of stochastic coupled system on networks are established. In addition, based on Lyapunov method and graph theory, global asymptotic stability criterion for the periodic solution is also given. Finally, a numerical example is provided to illustrate the effectiveness of the results developed.