TITLE:
A Seasonally Perturbed Prey-Predator Model with Smith Growth Rate
AUTHORS:
Qinggui Guo
KEYWORDS:
Smith Growth, Seasonal Perturbation, Hopf Bifurcation, Periodic Solution
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.16 No.4,
April
27,
2026
ABSTRACT: This paper investigates the dynamic behaviors of a predator-prey model with seasonal perturbations, incorporating the Smith growth pattern. First, for the unperturbed autonomous system, we conduct a detailed analysis of the existence and stability of equilibrium points, and derive the conditions under which a Hopf bifurcation occurs. Subsequently, taking into account seasonal variations in real ecosystems, we introduce a periodic perturbation by considering the prey growth rate as a time-dependent periodic function, thereby establishing a non-autonomous model. Moreover, we provide sufficient conditions for the existence of asymptotically stable periodic solutions. Numerical simulations are presented to validate the theoretical results.