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

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

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.

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.

Qualitative analysis of a diffusive predator–prey model with Allee and fear effects

2021 ◽  
pp. 2150037
Author(s):  
Jia Liu
Keyword(s):  
Allee Effect ◽  
Sufficient Conditions ◽  
Allee Effects ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Strong Allee Effect ◽  
Spatially Homogeneous ◽  
Fear Effects

In this study, we consider a diffusive predator–prey model with multiple Allee effects induced by fear factors. We investigate the existence, boundedness and permanence of the solution of the system. We also discuss the existence and non-existence of non-constant solutions. We derive sufficient conditions for spatially homogeneous (non-homogenous) Hopf bifurcation and steady state bifurcation. Theoretical and numerical simulations show that strong Allee effect and fear effect have great effect on the dynamics of system.

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