Pattern Formation in a Reaction-Diffusion Predator-Prey Model with Weak Allee Effect and Delay

Abstract

In this paper, we establish a reaction-diffusion predator-prey model with weak Allee effect and delay and analyze the conditions of Turing instability. The effects of Allee effect and delay on pattern formation are discussed by numerical simulation. The results show that pattern formations change with the addition of weak Allee effect and delay. More specifically, as Allee effect constant and delay increases, coexistence of spotted and stripe patterns, stripe patterns, and mixture patterns emerge successively. From an ecological point of view, we find that Allee effect and delay play an important role in spatial invasion of populations.

Population Dynamic Study of Prey-Predator Interactions with Weak Allee Effect, Fear Effect, and Delay

“…Dynamic complexities are the common characteristics in a variety of systems. e complexity of an ecosystem is reflected in both time and space [39,40]. From a biological point of view, this research shows that a weak Allee effect and gestation delay can destroy the stability of a species and lead to a decrease in population density.…”

Existence of W01,1Ω Solutions to Non-Coercivity Quasiline

“…e main difficulty of study is due to the a priori estimate of the sequence of the approximate solutions {푢 } of (18) in the non-reflexive space 푊 1,1 0 (Ω). For more results about existence of 푊 1,1 0 (Ω) to elliptic equations, see [23][24][25].…”

Pattern formation of parasite-host model induced by fear effect

“…It is not difficult to see that the above ordinary differential equations (74) have five equilibrium points, corresponding to five steady states 20,29,30,[33][34][35][36] . Considering the symmetry of the model, we have…”