Hopf bifurcation analysis in a multiple delayed innovation diffusion model with Holling II functional response

2019 ◽  
Vol 43 (4) ◽  
pp. 2056-2075
Author(s):  
Rakesh Kumar ◽  
Anuj Kumar Sharma ◽  
Kulbhushan Agnihotri
Keyword(s):  
Hopf Bifurcation ◽  
Functional Response ◽  
Innovation Diffusion ◽  
Diffusion Model ◽  
Bifurcation Analysis ◽  
Holling Ii Functional Response

Stability and Hopf Bifurcation Analysis of a Delayed Innovation Diffusion Model with Intra-Specific Competition

2021 ◽  
Vol 31 (14) ◽  
Author(s):  
Rakesh Kumar ◽  
Anuj Kumar Sharma
Keyword(s):  
Hopf Bifurcation ◽  
Innovation Diffusion ◽  
Diffusion Model ◽  
Normal Form Theory ◽  
Interior Equilibrium ◽  
Form Theory ◽  
Class Information ◽  
The Stability ◽  
Globally Stable ◽  
Information Class

This article is concerned with the diffusion of a sport in a region, and the innovation diffusion model comprising of population classes, viz. nonadopters class, information class and adopters class. A qualitative analysis is carried out to assess the global asymptotic stability of the interior equilibrium for null delay. It has also been proved that the parameter [Formula: see text] (age gaps among sportspersons) in the intra-specific competition between the new players and the senior players can even destabilize the otherwise globally stable interior equilibrium state and the coexistence of all the populations is possible through periodic solutions due to Hopf bifurcation. With the help of normal form theory and center manifold arguments, the stability of bifurcating periodic orbits is determined. Numerical simulations have been executed in support of the analytical findings.

Spatiotemporal Dynamics and Hopf Bifurcation in a Delayed Diffusive Intraguild Predation Model with Holling II Functional Response

2016 ◽  
Vol 26 (12) ◽  
pp. 1650197 ◽  
Author(s):  
Renji Han ◽  
Binxiang Dai
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Functional Response ◽  
Intraguild Predation ◽  
Functional Differential Equations ◽  
Spiral Wave ◽  
Wave Pattern ◽  
Center Manifold Reduction ◽  
Functional Differential ◽  
Holling Ii Functional Response

We propose a kind of delayed diffusive intraguild predation model with Holling II functional response in this paper. By analyzing the eigenvalue spectrum, it is found that the stability or instability of equilibria can be induced by delay. By utilizing the local bifurcation theory of partial functional differential equations, Hopf bifurcation of the proposed system with time delay as bifurcation parameter is investigated. It reveals that the time delay has a destabilizing effect in the intraguild predation model dynamics and a phenomenon of Hopf bifurcation occurs when the delay increases through a certain threshold. Then we give the explicit formulas to determine the direction, stability of Hopf bifurcation by utilizing the normal form method and center manifold reduction for PFDEs. Numerical simulations are performed to illustrate our theoretical results and show that delay and diffusion can induce the system into chaos and even trigger the emergence of different types of spatial patterns, including spiral wave pattern and chaotic wave pattern, which are induced by Hopf instability.

Bifurcation analysis in a host-generalist parasitoid model with Holling II functional response

2020 ◽  
Vol 268 (8) ◽  
pp. 4618-4662 ◽  
Author(s):  
Chuang Xiang ◽  
Jicai Huang ◽  
Shigui Ruan ◽  
Dongmei Xiao
Keyword(s):  
Functional Response ◽  
Bifurcation Analysis ◽  
Holling Ii Functional Response
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