Dynamic Analysis on a Diffusive Two‐Enterprise Interaction Model with Two Delays

The oscillation and instability of systems caused by time delays have been widely studied over the past several decades. In nature, the phenomenon of diffusion is universal. Therefore, it is necessary to investigate the dynamic behavior of reaction-diffusion systems with time delays. In this study, a two-enterprise interaction model with diffusion and delay effects is considered. By analyzing the distribution of the roots of the corresponding characteristic equation, some conditions for the stability of the unique positive equilibrium and the existence of Hopf bifurcation at the steady state are investigated. As the sum of the time delays changes, there are a series of periodic solutions at the trivial steady-state solution of the system. In addition, the direction of Hopf bifurcation and the stability of the periodic solutions are discussed by using the normal form theory and the center manifold reduction of partial functional differential equations. Finally, numerical simulation experiments are conducted to illustrate the validity of the theoretical conclusions.