TITLE:
Population Dynamics System with Time Delay and Taxis
AUTHORS:
Yangxu Wei
KEYWORDS:
Predator-Prey Model, Chemotaxis, Time Delay, Hopf Bifurcation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.7,
July
17,
2026
ABSTRACT: This paper investigates a class of population dynamics models incorporating prey-taxis, a complex density-dependent functional response, and a time delay in predation conversion. The main purpose of this paper is to explore the effect of time delay on the spatiotemporal dynamic evolution of the system. By fixing the taxis coefficient and conducting a detailed analysis of the characteristic equation of the system at the positive equilibrium point, we treat the time delay
τ
as the bifurcation parameter, provide sufficient conditions for the local asymptotic stability of the positive equilibrium point in the ODE model, and rigorously prove that delay-induced Hopf bifurcations occur when
τ
crosses a series of critical thresholds. Finally, numerical simulations verify the correctness of the theoretical analysis. The results indicate that even in a system with spatial diffusion and taxis, a relatively large time delay will destroy the steady-state coexistence of populations, thereby triggering sustained periodic oscillations in predator and prey densities.