Bifurcation and chaos in a host-parasitoid model with a lower bound for the host

Abstract

In this paper, a discrete-time biological model and its dynamical behaviors are studied in detail. The existence and stability of the equilibria of the model are qualitatively discussed. More precisely, the conditions for the existence of a flip bifurcation and a Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. Numerical simulations are presented not only to validate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors. We also analyze the dynamic characteristics of the system in a two-dimensional parameter space. Numerical results indicate that we can more clearly and directly observe the chaotic phenomenon, period-doubling and period-adding, and the optimal parameters matching interval can also be found easily.

A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control

“…Liu et al [18] explored a complex behavior and bifurcation analysis for a class of host-parasitoid interaction with an application of the Allee effect and Holling type III functional response. Moreover, in [19], chaos control and bifurcation analysis were studied for a host-parasitoid model with a lower bound for the host. In [20] and [21], the influence of a refuge effect was explored for certain classes of host-parasitoid models.…”

Stability of a certain class of a host–parasitoid models with a spatial refuge effect

“…Many authors have investigated different types of discrete host-parasitoid models under different ecological factors and different assumptions, see for example [1,7,[12][13][14][18][19][20][21]23,24,28].…”

Dynamic complexity and bifurcation analysis of a host–parasitoid model with Allee effect and Holling type III functional response

“…In contrast, populations with weak Allee effects do not have this threshold. Recently, researchers have focused on the Allee effect on different ecosystems, including discrete-time systems [2][3][4][5][6][7] and continuous-time systems [8][9][10][11][12][13][14]. Zhao and Lv [15] study the dynamic complexity of a host-parasitoid system with a lower bound for host, and the form of Allee effect is H(t)-n H(t)+m , where m is an Allee effect constant, n is the lower bound for the host.…”

“…where b, c are the parameters related to the Holling type III functional response bTH(t)P(t) 1+cH(t)+bT n H(t) 2 , and b > 0 is a conversion factor, c = aT n . The outline of this paper is as follows.…”

“…Therefore f UU = 2a 200 a 010 + 2a 110 (μa 100 ) + 2a 020 (μa 100 ) 2 a 010 , f UV = -a 110 ω -2a 020 ω(μa 100 ) a 010 , f VV = 2a 020 ω 2 a 010 , f UUU = 6a 300 a 2 010 + 6a 210 a 010 (μa 100 ) + 6a 120 (μa 100 ) 2 + 6a 030 (μa 100 ) a 010 ,…”