scholarly journals The Connection Matrix analysis of a Prey-Predator system with a Strong Allee effect and multiple interior equilibria

2021 ◽  
Author(s):  
Asim Sikder
Keyword(s):  
Functional Response ◽  
Death Rate ◽  
Allee Effect ◽  
Matrix Theory ◽  
Matrix Analysis ◽  
Connection Matrix ◽  
Connecting Orbits ◽  
Strong Allee Effect ◽  
Predator System ◽  
Robust Permanence

Abstract We consider a Gause-type prey-predator system incorporating a strong allee effect for the prey population. For the existence of multiple interior equilibria we consider Holling-type predator functional response and the density dependent death rate for the predator. With the help of the Conley connection matrix theory we study the dynamics of the system in presence of one, two and three interior equilibria. It is found that (i) the saddle-saddle connections exist in presence of single and multiple interior equilibria connecting interior flows to the boundary and (ii) the system admits a set of degree-2 (i.e, a 2-discs of) connecting orbits from interior equlibrium to the origin. Thus permanence or robust permanence of the system is not possible.

scholarly journals Multiple Bifurcations and Chaos in a Discrete Prey-Predator System with Generalized Holling III Functional Response

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Xia Liu ◽  
Yanwei Liu ◽  
Qiaoping Li
Keyword(s):  
Numerical Methods ◽  
Functional Response ◽  
Bifurcation Theory ◽  
Allee Effect ◽  
Center Manifold ◽  
Step Size ◽  
Center Manifold Theorem ◽  
Strong Allee Effect ◽  
Holling Iii Functional Response ◽  
Predator System

A prey-predator system with the strong Allee effect and generalized Holling type III functional response is presented and discretized. It is shown that the combined influences of Allee effect and step size have an important effect on the dynamics of the system. The existences of Flip and Neimark-Sacker bifurcations and strange attractors and chaotic bands are investigated by using the center manifold theorem and bifurcation theory and some numerical methods.

Dynamics of a Prey–Predator System with Herd Behaviour in Both and Strong Allee Effect in Prey

BIOPHYSICS ◽  
2020 ◽  
Vol 65 (5) ◽  
pp. 826-835
Author(s):  
S. Biswas ◽  
D. Pal ◽  
G. S. Mahapatra ◽  
G. P. Samanta
Keyword(s):  
Allee Effect ◽  
Strong Allee Effect ◽  
Herd Behaviour ◽  
Predator System

Rich Global Dynamics in a Prey–Predator Model with Allee Effect and Density Dependent Death Rate of Predator

2015 ◽  
Vol 25 (03) ◽  
pp. 1530007 ◽  
Author(s):  
Moitri Sen ◽  
Malay Banerjee
Keyword(s):  
Death Rate ◽  
Allee Effect ◽  
Growth Function ◽  
Global Dynamics ◽  
Density Dependent ◽  
Strong Allee Effect ◽  
Local And Global Bifurcations ◽  
Predator Model ◽  
Type Ii Functional Response ◽  
Comprehensive Study

In this work we have considered a prey–predator model with strong Allee effect in the prey growth function, Holling type-II functional response and density dependent death rate for predators. It presents a comprehensive study of the complete global dynamics for the considered system. Especially to see the effect of the density dependent death rate of predator on the system behavior, we have presented the two parametric bifurcation diagrams taking it as one of the bifurcation parameters. In course of that we have explored all possible local and global bifurcations that the system could undergo, namely the existence of transcritical bifurcation, saddle node bifurcation, cusp bifurcation, Hopf-bifurcation, Bogdanov–Takens bifurcation and Bautin bifurcation respectively.

A delayed prey–predator system with prey subject to the strong Allee effect and disease

2016 ◽  
Vol 84 (3) ◽  
pp. 1569-1594 ◽  
Author(s):  
Santanu Biswas ◽  
Md. Saifuddin ◽  
Sourav Kumar Sasmal ◽  
Sudip Samanta ◽  
Nikhil Pal ◽  
...  
Keyword(s):  
Allee Effect ◽  
Strong Allee Effect ◽  
Predator System

Bifurcation Analysis of a Prey–Predator Model with Beddington–DeAngelis Type Functional Response and Allee Effect in Prey

2020 ◽  
Vol 30 (16) ◽  
pp. 2050238
Author(s):  
Koushik Garain ◽  
Partha Sarathi Mandal
Keyword(s):  
Functional Response ◽  
Death Rate ◽  
Allee Effect ◽  
Equilibrium Points ◽  
Growth Function ◽  
Global Dynamics ◽  
Density Dependent ◽  
Existence And Stability ◽  
Predator Model ◽  
The Impact

The article aims to study a prey–predator model which includes the Allee effect phenomena in prey growth function, density dependent death rate for predators and Beddington–DeAngelis type functional response. We notice the changes in the existence and stability of the equilibrium points due to the Allee effect. To investigate the complete global dynamics of the Allee model, we present here a two-parametric bifurcation diagram which describes the effect of density dependent death rate parameter of predator on dynamical changes of the system. We have also analyzed all possible local and global bifurcations that the system could go through, namely transcritical bifurcation, saddle-node bifurcation, Hopf-bifurcation, cusp bifurcation, Bogdanov–Takens bifurcation and homoclinic bifurcation. Finally, the impact of the Allee effect in the considered system is investigated by comparing the dynamics of both the systems with and without Allee effect.

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