Dynamic behavior of taxis-driven intraguild predation model of three species with BD functional response

Abstract

In this paper, we study a chemotaxis-based model for three-species intraguild predation model. We present global boundedness of classical solutions in any dimension without any restrictions on initial data and $\chi$. Moreover, it is asserted that the considered system will approach prey-only steady state and semi-coexistence steady state in the large time limit. Finally, using the spectral analysis, we investigate the effect of Beddington-deAngelis type production term on the stability and instability of a linearized problem around the coexistence steady state, and we then extend our analysis to the nonlinear system, which makes up for the stability of coexistence steady state. Additionally, we apply our theoretical results to several concrete Holling type II functions, discuss the theoretical conditions through numerical simulations, and verify the predictions of our analysis.