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

Abstract

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.

Bifurcations in a Plant-Pollinator Model with Multiple Delays

“…However, in these existing mathematical models, most researchers did not consider the time delay factor. Due to its inevitability and importance, the infuence of time delay on dynamic behavior has been adequately considered in some models, such as the predator-prey model [10][11][12][13][14], the competition and cooperation model of two enterprises [15][16][17][18][19], the neuron network model [20][21][22], the competition model of internet [23,24], the chemical reaction model [25,26], and the epidemic model [27][28][29][30][31]. Te introduction of the delay factor can more accurately refect the objective facts and development laws of things.…”

The Existence of Periodic Solutions for a Two-Enterprise Interaction Model with Delays

“…Recently, many researchers have investigated the dynamics of the enterprise mathematical models from biological point of view and described the development progress. One can also forecast the growth tendency of enterprises by analyzing the dynamics of the models [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. For example, in [1], assume that the interaction between two enterprises are continuous and the outputs of two *Corresponding author: E-mail: cfeng@alasu.edu ; enterprises satisfy a certain relation between resource and consumers, Xu proposed the following model:…”