Uniform persistence and multistability in a two-predator–one-prey system with inter-specific and intra-specific competition

2021 ◽  
Author(s):  
Yuhua Long ◽  
Lin Wang ◽  
Jia Li
Keyword(s):  
Uniform Persistence ◽  
Prey System

scholarly journals Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Kankan Sarkar ◽  
Subhas Khajanchi ◽  
Prakash Chandra Mali ◽  
Juan J. Nieto
Keyword(s):  
Growth Rate ◽  
Hopf Bifurcation ◽  
Dynamical Behavior ◽  
Prey Population ◽  
Uniform Persistence ◽  
Functional Responses ◽  
Normal Form Theory ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Prey System

In this study, we investigate a mathematical model that describes the interactive dynamics of a predator-prey system with different kinds of response function. The positivity, boundedness, and uniform persistence of the system are established. We investigate the biologically feasible singular points and their stability analysis. We perform a comparative study by considering different kinds of functional responses, which suggest that the dynamical behavior of the system remains unaltered, but the position of the bifurcation points altered. Our model system undergoes Hopf bifurcation with respect to the growth rate of the prey population, which indicates that a periodic solution occurs around a fixed point. Also, we observed that our predator-prey system experiences transcritical bifurcation for the prey population growth rate. By using normal form theory and center manifold theorem, we investigate the direction and stability of Hopf bifurcation. The biological implications of the analytical and numerical findings are also discussed in this study.

scholarly journals Boundedness and Global Stability for a Predator-Prey System with the Beddington-DeAngelis Functional Response

2010 ◽  
Vol 2010 ◽  
pp. 1-24 ◽  
Author(s):  
Wahiba Khellaf ◽  
Nasreddine Hamri
Keyword(s):  
Global Stability ◽  
Functional Response ◽  
Qualitative Behavior ◽  
Uniform Persistence ◽  
Boundedness Of Solutions ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Prey System ◽  
Predator Prey Models ◽  
Type Ii Functional Response

We study the qualitative behavior of a class of predator-prey models with Beddington-DeAngelis-type functional response, primarily from the viewpoint of permanence (uniform persistence). The Beddington-DeAngelis functional response is similar to the Holling type-II functional response but contains a term describing mutual interference by predators. We establish criteria under which we have boundedness of solutions, existence of an attracting set, and global stability of the coexisting interior equilibrium via Lyapunov function.

Uniform persistence for a discrete predator–prey system with delays

2011 ◽  
Vol 218 (4) ◽  
pp. 1174-1179 ◽  
Author(s):  
Xitao Yang ◽  
Yaqin Liu ◽  
Jing Chen
Keyword(s):  
Uniform Persistence ◽  
Predator Prey ◽  
Prey System

Study of refuge use on a predator–prey system with a competitor for the prey

2017 ◽  
Vol 10 (02) ◽  
pp. 1750023 ◽  
Author(s):  
Debasis Mukherjee
Keyword(s):  
Sufficient Conditions ◽  
Critical Value ◽  
Positive Equilibrium ◽  
Uniform Persistence ◽  
Type Ii ◽  
Asymptotically Stable ◽  
Prey Refuge ◽  
Refuge Use ◽  
Predator Prey ◽  
Prey System

In this paper, we propose a predator–prey system with a competitor for the prey. The model incorporates a constant prey refuge and predation process follows Holling type II response function. Using the Routh–Hurwitz criterion, the sufficient conditions of locally asymptotically stable of all the equilibria are obtained. Furthermore, global stability of the positive equilibrium is investigated by constructing a suitable Lyapunov function. The occurrence of Hopf-bifurcation of the system is shown at a critical value “[Formula: see text]” and the system can be stabilized by increasing amount of prey refuge. The result includes the sufficient conditions for uniform persistence. Numerical simulations are carried out to illustrate the obtained results and the dependence of the dynamic behavior on the prey refuge.

Sign in / Sign up

Export Citation Format

Share Document