A hybrid predator–prey model with general functional responses under seasonal succession alternating between Gompertz and logistic growth

Abstract

In this paper, a hybrid predator–prey model with two general functional responses under seasonal succession is proposed. The model is composed of two subsystems: in the first one, the prey follows the Gompertz growth, and it turns to the logistic growth in the second subsystem since seasonal succession. The two processes are connected by impulsive perturbations. Some very general, weak criteria on the ultimate boundedness, permanence, existence, uniqueness and global attractivity of predator-free periodic solution are established. We find that the hybrid population model with seasonal succession has more survival possibilities of natural species than the usual population models. The theoretical results are illustrated by special examples and numerical simulations.

Modelling Predator–Prey Interactions: A Trade-Off between Seasonality and Wind Speed

“…In the field of theoretical ecology, a sufficient number of studies have been performed in this context, but in mathematical ecology, less attention has been paid paid. Some research has been performed by considering temperature as an abiotic factor [4]. However, this leaves a knowledge deficit about how other abiotic elements affect the interactions among ecological communities.…”

Existence theory and numerical analysis of three species prey–predator model under Mittag-Leffler power law

“…Most of the published work describes the mathematical system of predators and prey as a problem of Cauchy type of a system of classical differential equations [21][22][23][24][25]. However, recently, there has been great interest in studying the behavior of the solution for some biological systems using fractional differential equations involving the Atangana-Baleanu operator by several authors for the purpose of investigating several real-world systems and modeling infectious diseases; see [26][27][28][29][30][31][32][33][34][35][36].…”