Qualitative behavior of a diffusive predator–prey–mutualist model

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Yaying Dong ◽  
Shanbing Li
Keyword(s):  
Qualitative Behavior ◽  
Predator Prey

scholarly journals CODIMENSION TWO BIFURCATIONS IN A PREDATOR–PREY SYSTEM WITH GROUP DEFENSE

2001 ◽  
Vol 11 (08) ◽  
pp. 2123-2131 ◽  
Author(s):  
DONGMEI XIAO ◽  
SHIGUI RUAN
Keyword(s):  
Homoclinic Bifurcation ◽  
Qualitative Behavior ◽  
Homoclinic Loop ◽  
Saddle Node Bifurcation ◽  
Predator Prey ◽  
Codimension Two ◽  
Prey System ◽  
Group Defense ◽  
Nonmonotonic Functional Response ◽  
Parameter Values

In this paper we study the qualitative behavior of a predator–prey system with nonmonotonic functional response. The system undergoes a series of bifurcations including the saddle-node bifurcation, the supercritical Hopf bifurcation, and the homoclinic bifurcation. For different parameter values the system could have a limit cycle or a homoclinic loop, or exhibit the so-called "paradox of enrichment" phenomenon. In the generic case, the model has the bifurcation of cusp-type codimension two (i.e. the Bogdanov–Takens bifurcation) but no bifurcations of codimension three.

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.

scholarly journals Analytical Study of a System of Dierence Equation

2019 ◽  
pp. 1-18
Author(s):  
Abdualrazaq Sanbo ◽  
Elsayed M. Elsayed
Keyword(s):  
Analytical Study ◽  
Initial Conditions ◽  
Qualitative Behavior ◽  
Real Numbers ◽  
Positive Real ◽  
Predator Prey ◽  
Rational Difference Equations ◽  
Predator Prey Model ◽  
Special Cases ◽  
Theoretical Results

We study the qualitative behavior of a predator-prey model, where the carrying capacity of the predators environment is proportional to the number of prey. The considered system is given by the following rational difference equations: where the initial conditions x-2; x-1; x0; y-2; y-1; y0 are arbitrary positive real numbers. Also, we give specic form of the solutions of some special cases of this equation. Some numerical examples are given to verify our theoretical results.

Qualitative behavior of predator-prey communities

1977 ◽  
Vol 65 (1) ◽  
pp. 101-132 ◽  
Author(s):  
Juan Lin ◽  
Peter B. Kahn
Keyword(s):  
Qualitative Behavior ◽  
Predator Prey

scholarly journals Qualitative effects of introducing nonlinear birth and death rates for the predator in a predator-prey type model

BIOMATH ◽  
2017 ◽  
Vol 6 (1) ◽  
pp. 1703167
Author(s):  
Tihomir B. Ivanov ◽  
Neli S. Dimitrova
Keyword(s):  
Equilibrium Points ◽  
Classical Model ◽  
Uniform Boundedness ◽  
Prey Type ◽  
Type Model ◽  
Qualitative Behavior ◽  
Death Rates ◽  
Predator Prey ◽  
Stability And Bifurcations ◽  
Predator Behavior

In this paper, we study how introducing nonlinear birth and death rates for the predator might affect the qualitative behavior of a mathematical model, describing predator-prey systems. We base our investigations on a known model, exhibiting anti-predator behavior. We propose a generalization of the latter by introducing generic birth and death rates for the predator and study the dynamics of the resulting system. We establish existence and uniqueness of positive model solutions, their uniform boundedness, existence, local stability and bifurcations of equilibrium points as well as global stability properties of the solutions. Most of the solution properties are demonstrated numerically and graphically by various numerical examples. Based on the obtained results, we show that the model with nonlinear birth and death rates can describe a much more complex behavior of the predator-prey system than the classical model (i.e., with linear rates) does.

ROLE OF DISEASE PROPAGATION IN MIGRATORY BIRD POPULATION

2012 ◽  
Vol 05 (03) ◽  
pp. 1260002
Author(s):  
SHUJING GAO ◽  
YUMIN DING ◽  
JIANPING XIE
Keyword(s):  
Functional Response ◽  
Predation Rate ◽  
Migratory Bird ◽  
Vital Role ◽  
Recruitment Rate ◽  
Qualitative Behavior ◽  
Predator Prey ◽  
Disease Propagation ◽  
Predator Prey Model ◽  
Nonlinear Anal

Chatterjee considered a predator–prey model with avian migration in the migration prey population [S. Chatterjee, Alternative prey source coupled with prey recovery enhance stability between migratory prey and their predator in the presence of disease, Nonlinear Anal. Real World Appl. 11 (2010) 4415–4430]. In this paper, we modify and analyze the model by taking time dependent parameters and the general functional response into consideration. The conditions for the persistence of the system and the extinction of the disease are obtained. The global attractivity of the system is also studied. By numerical simulations, we find that the qualitative behavior of the system independent on the choice of the functional response. Moreover, it is observed that the infection rate, recruitment rate and the predation rate play a vital role in predicting the behavior of the dynamics.

scholarly journals Stability and bifurcations of a discrete-time prey-predator system with constant prey refuge

2021 ◽  
Vol 2070 (1) ◽  
pp. 012068
Author(s):  
A George Maria Selvam ◽  
R Janagaraj ◽  
S Britto Jacob ◽  
D Vignesh
Keyword(s):  
Jacobian Matrix ◽  
Chaotic Behavior ◽  
Existence Results ◽  
Qualitative Behavior ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Stability And Bifurcations ◽  
The Stability ◽  
Predator System

Abstract In ecology, by refuge an organism attains protection from predation by hiding in an area where it is unreachable or cannot simply be found. In population dynamics, once refuges are available, both prey-predator populations are expressively greater and meaningfully extra species can be sustained in the region. This examine the stability of a discrete predator prey model incorporating with constant prey refuge. Existence results and the stability conditions of the system are analyzed by obtaining fixed points and Jacobian matrix. The chaotic behavior of the system is discussed with bifurcation diagrams. Numerical experiments are simulated for the better understanding of the qualitative behavior of the considered model. Mathematics Subject Classification. [2010] : 37C25, 39A28, 39A30, 92D25.

Cognition in predator-prey systems: Searching image and prey polymorphism

1997 ◽  
Author(s):  
Alan B. Bond ◽  
Alan C. Kamil ◽  
Christopher Cink
Keyword(s):  
Predator Prey
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