Dynamical behaviour of a generalist predator-prey model with free boundary

Abstract

In this paper, we consider a free boundary problem describing the invasion of a generalist predator into a prey population. We analytically derive the conditions guaranteeing the existence and uniqueness of the classical solution by means of the Schauder fixed point theorem, and further study the long-time behaviours of these two species. Finally, we numerically investigate the dynamical behaviour during the early invasion stage. Numerical results show that generalist predators are more likely to succeed in alien invasion by reducing the threshold size of the spatial domain of initial invasion, below which invasion fails.

A Lycaon pictus impulsive state feedback control model with Allee effect and continuous time delay

“…In recent years, impulsive differential equations have been used in various fields [12][13][14][15][16][17][18][19][20], such as disease control and pharmacology [21][22][23][24][25][26][27][28][29], integrated pest management [30][31][32][33][34][35][36][37][38], microbial culture [38][39][40][41][42][43], and protection of endangered animals and plants [44][45][46][47][48][49][50][51]. For example, Zhang et al [10] focused on a predator-prey model with impulsive state feedback control and assuming that the spraying pesticide and releasing the natural enemies are taken at different thresholds.…”

Permanence, stability, and coexistence of a diffusive predator–prey model with modified Leslie–Gower and B–D functional response

“…Many scholars have studied predator-prey models with different functional responses from different views. For example, Wang et al [18] and Cheng et al [19] considered the Holling I type functional response in a predator-prey model, Ko and Ryu [20] focused on the Holling II type functional response, Zhuo and Zhang [21], Pang and Wang [22], and Wang [23] investigated the ratio-dependent predator-prey system, and other functional response, please see [24][25][26][27][28][29].…”

Bifurcation analysis in a diffusive predator–prey system with Michaelis–Menten-type predator harvesting

“…In nature, predation relationship plays a very important role in ecosystems. Many scholars studied predator-prey dynamic models and developed them in many ways [1][2][3][4][5][6][7][8][9]. Bian et al [10] proposed a stochastic prey-predator system in a polluted environment with Beddington-DeAngelis functional response and derived sufficient conditions for the existence of boundary periodic solutions and positive periodic solutions.…”