Analysis of dynamic properties on forest restoration-population pressure model

Abstract

<abstract> <p>On the basis of logistic models of forest restoration, we consider the influence of population pressure on forest restoration and establish a reaction diffusion model with Holling Ⅱ functional responses. We study this reaction diffusion model under Dirichlet boundary conditions and obtain a positive equilibrium. In the square region, we analyze the existence of Turing instability and Hopf bifurcation near this point. The square patterns and mixed patterns are obtained when steady-state bifurcation occurs, the hyperhexagonal patterns appears in Hopf bifurcation.</p> </abstract>

Dynamic analysis of a Leslie–Gower-type predator–prey system with the fear effect and ratio-dependent Holling III functional response

“…As one of the most common mutual relationships between two populations in nature, predator-prey relationship plays a significant role in ecology and mathematical biology [2]. Since the dynamic behaviours of predator-prey models were formulated by Lotka and Volterra, many experts and scholars have studied various types of predator-prey models over the past decades, thus establishing the theoretical basis for interspecific interactions [1,4,12,14]. In 1948, Leslie and Gower introduced a functional response called Leslie-Gower, which was based on the Logistic model proposed by Verhulst.…”