Journal ArticleDOI
Hopf bifurcation of a ratio-dependent predator–prey system with time delay
TLDR
In this paper, a ratio dependent predator-prey system with time delay was considered, where the dynamics was logistic with the carrying capacity proportional to the prey population, and the stability and Hopf bifurcation of the system based on the normal form approach and the center manifold theory was analyzed.Abstract:
In this paper, we consider a ratio dependent predator–prey system with time delay where the dynamics is logistic with the carrying capacity proportional to prey population. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the system based on the normal form approach and the center manifold theory. Finally, we illustrate our theoretical results by numerical simulations.read more
Citations
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Journal ArticleDOI
Hopf bifurcation and topological horseshoe of a novel finance chaotic system
Chao Ma,Xingyuan Wang +1 more
TL;DR: In this article, the existence of both Hopf bifurcation and topological horseshoe for a novel finance chaotic system has been investigated through rigorous mathematical analysis, and it is shown that a Hopf partition occurs at systems' three equilibriums S0, 1, 2 and Hopfbifurcation at equilibrium S0 is non-degenerate and supercritical.
Journal ArticleDOI
On the stability and Hopf bifurcation of a delay-induced predator–prey system with habitat complexity
Nandadulal Bairagi,Debaldev Jana +1 more
TL;DR: In this article, the effect of the degree of habitat complexity and gestation delay on the stability of a predator-prey model was studied. But the authors did not consider the relationship between the delay and the abundance of the population.
Journal ArticleDOI
The Hopf bifurcation and stability of delayed predator–prey system
TL;DR: In this paper, a mathematical model consisting of three populations with discrete time delays is considered and the local stability of each of the feasible equilibria of the system is addressed and the existence of Hopf bifurcations at the coexistence equilibrium is established.
Journal ArticleDOI
Species coexistence and chaotic behavior induced by multiple delays in a food chain system
Zigen Song,Bin Zhen,Jian Xu +2 more
TL;DR: Greater RDD and CDD make system population enter into system collapse easier, and complex dynamical behaviors including multiple periodic motion and chaotic behavior are exhibited in detail.
Journal ArticleDOI
Stability and Hopf bifurcation analysis of a ratio-dependent predator-prey model with two time delays and Holling type III functional response
Xuedi Wang,Miao Peng,Xiuyu Liu +2 more
TL;DR: A delayed ratio-dependent predator-prey model with Holling type III functional response and stage structure for the predator is considered and the existence of Hopf bifurcations at the coexistence equilibrium is established.
References
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Book
Delay Differential Equations: With Applications in Population Dynamics
TL;DR: Delay Differential Equations as mentioned in this paper are a generalization of delay differential equations and have been used in a variety of applications in population dynamics, such as global stability for single species models and multi-species models.
Book
Theory and applications of Hopf bifurcation
TL;DR: The Hopf Bifurcation Theorum has been used in many applications, such as Differential Difference and Integro-differential Equations (by hand).
Journal ArticleDOI
Discrete delay, distributed delay and stability switches
Kenneth L. Cooke,Zvi Grossman +1 more
TL;DR: In this article, the authors examine how the stability properties of certain models change when the delay is increased and show that there may be arbitrarily many switches from stability to instability to stability, but in (1) this is not possible.
Journal ArticleDOI
Complex dynamic behaviors of a discrete-time predator-prey system
Xiaoli Liu,Dongmei Xiao +1 more
TL;DR: In this paper, the dynamics of a discrete-time predator-prey system is investigated in the closed first quadrant R + 2, and it is shown that the system undergoes flip bifurcation and Hopf bifurbation in the interior of R+2 by using center manifold theorem and bifurlcation theory.
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