Dynamics of a Leslie-Gower predator-prey system with hunting cooperation and prey harvesting

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yong Yao ◽  
Lingling Liu
Keyword(s):  
Complex Dynamics ◽  
Critical Values ◽  
Predator Population ◽  
Predator Prey ◽  
Codimension Two ◽  
Prey System ◽  
Constant Rate ◽  
Risk Of Extinction ◽  
Parameter Values ◽  
Theoretical Results

<p style='text-indent:20px;'>In this paper, we study the dynamics of a Leslie-Gower predator-prey system with hunting cooperation among predator population and constant-rate harvesting for prey population. It is shown that there are a weak focus of multiplicity up to three and a cusp of codimension at most two for various parameter values, and the system exhibits two saddle-node bifurcations, a Bogdanov-Takens bifurcation of codimension two and a Hopf bifurcation as the bifurcation parameters vary. The results developed in this article reveal far more complex dynamics compared to the Leslie-Gower system and show how the prey harvesting and the hunting cooperation affect the dynamics of the system. In particular, there exist some critical values of prey harvesting and hunting cooperation such that the predator and prey populations are at risk of extinction if the intensities of harvesting and hunting cooperation are greater than these critical values. Moreover, numerical simulations are presented to illustrate our theoretical results.</p>

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 Complex Dynamics in a Singular Delayed Bioeconomic Model with and without Stochastic Fluctuation

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Xinyou Meng ◽  
Qingling Zhang
Keyword(s):  
Hopf Bifurcation ◽  
Complex Dynamics ◽  
Hybrid Control ◽  
Positive Equilibrium ◽  
Stochastic Fluctuation ◽  
Predator Prey ◽  
Prey System ◽  
Singularity Induced Bifurcation ◽  
Distribution Of Roots ◽  
Theoretical Results

A singular delayed biological economic predator-prey system with and without stochastic fluctuation is proposed. The conditions of singularity induced bifurcation are gained, and a state feedback controller is designed to eliminate such bifurcation. Furthermore, saddle-node bifurcation is also showed. Next, the local stability of the positive equilibrium and the existence of Hopf bifurcation are obtained by analyzing the distribution of roots of the corresponding characteristic equation, and the hybrid control strategy is used to control the occurrence of Hopf bifurcation. In addition, some explicit formulas determining the spectral densities of the populations and harvest effort are given when the system is considered with stochastic fluctuation. Finally, numerical simulations are illustrated to verify the theoretical results.

Complex Dynamics of an Eco-Epidemic System with Disease in Prey Species

2021 ◽  
Vol 31 (03) ◽  
pp. 2150046
Author(s):  
Absos Ali Shaikh ◽  
Harekrishna Das ◽  
Nijamuddin Ali
Keyword(s):  
Prey Species ◽  
Complex Dynamics ◽  
Period Doubling ◽  
Alternative Food ◽  
Predator Population ◽  
Free System ◽  
Predator Prey ◽  
Force Of Infection ◽  
Prey System ◽  
Half Saturation Constant

The objective of this study is to investigate the complex dynamics of an eco-epidemic predator–prey system where disease is transmitted in prey species and predator population is being provided with alternative food. Holling type-II functional response is taken into consideration for interaction of predator and prey species. The half saturation constant for infected prey, the growth rate of susceptible prey and force of infection play a significant role to create complex dynamics in this predator–prey system where alternative food is present. It is seen that healthy disease-free system is possible here. The system shows some important dynamics viz. stable coexistence, Hopf bifurcation, period-doubling bifurcation and chaos. The analytical results obtained from the model are justified numerically.

BIFURCATION ANALYSIS OF A LOGISTIC PREDATOR–PREY SYSTEM WITH DELAY

2016 ◽  
Vol 57 (4) ◽  
pp. 445-460
Author(s):  
CANAN ÇELİK ◽  
GÖKÇEN ÇEKİÇ
Keyword(s):  
Delay Time ◽  
Critical Values ◽  
Normal Form Theory ◽  
Predator Prey ◽  
System With Delay ◽  
Prey System ◽  
Form Theory ◽  
Bifurcating Periodic Solution ◽  
Centre Manifold Theorem ◽  
Theoretical Results

We consider a coupled, logistic predator–prey system with delay. Mainly, by choosing the delay time${\it\tau}$as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay time${\it\tau}$passes some critical values. Based on the normal-form theory and the centre manifold theorem, we also derive formulae to obtain the direction, stability and the period of the bifurcating periodic solution at critical values of ${\it\tau}$. Finally, numerical simulations are investigated to support our theoretical results.

scholarly journals Numerical Solution of a Class of Predator-Prey Systems with Complex Dynamics Characters Based on a Sinc Function Interpolation Collocation Method

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-34
Author(s):  
Mingjing Du ◽  
Pengfei Ning ◽  
Yulan Wang
Keyword(s):  
Collocation Method ◽  
Complex Dynamics ◽  
Sinc Function ◽  
New Approach ◽  
Predator Prey ◽  
Prey System ◽  
Simulation Results ◽  
Pattern Formations ◽  
Theoretical Results ◽  
Good Agreement

Although many kinds of numerical methods have been announced for the predator-prey system, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, in this paper, a new interpolation collocation method is proposed for a class of predator-prey systems with complex dynamics characters. Some complex dynamics characters and pattern formations are shown by using this new approach, and the results have a good agreement with theoretical results. Simulation results show the effectiveness of the method.

scholarly journals Cooperative hunting in a discrete predator–prey system

2020 ◽  
Vol 13 (07) ◽  
pp. 2050063
Author(s):  
Yunshyong Chow ◽  
Sophia R.-J. Jang ◽  
Hua-Ming Wang
Keyword(s):  
Growth Rate ◽  
Discrete Time ◽  
Reproductive Number ◽  
Model Parameters ◽  
Predator Population ◽  
Sufficient Condition ◽  
Predator Prey ◽  
Cooperative Hunting ◽  
Prey System ◽  
Dependent Growth

We propose and investigate a discrete-time predator–prey system with cooperative hunting in the predator population. The model is constructed from the classical Nicholson–Bailey host-parasitoid system with density dependent growth rate. A sufficient condition based on the model parameters for which both populations can coexist is derived, namely that the predator’s maximal reproductive number exceeds one. We study existence of interior steady states and their stability in certain parameter regimes. It is shown that the system behaves asymptotically similar to the model with no cooperative hunting if the degree of cooperation is small. Large cooperative hunting, however, may promote persistence of the predator for which the predator would otherwise go extinct if there were no cooperation.

EFFECT OF VIRAL INFECTION ON THE GENERALIZED GAUSE MODEL OF PREDATOR-PREY SYSTEM

2003 ◽  
Vol 11 (01) ◽  
pp. 19-26 ◽  
Author(s):  
J. CHATTOPADHYAY ◽  
A. MUKHOPADHYAY ◽  
P. K. ROY
Keyword(s):  
Viral Infection ◽  
Specific Growth ◽  
Dynamical Behavior ◽  
Prey Population ◽  
Predator Population ◽  
Predator Prey ◽  
Stability Behavior ◽  
Force Of Infection ◽  
Prey System ◽  
Infected Prey

The generalized Gause model of predator-prey system is revisited with an introduction of viral infection on prey population. Stability behavior of such modified system is carried out to observe the change of dynamical behavior of the system. To substantiate the analytical results of this generalized susceptible prey, infected prey and predator population, numerical simulations of the model with specific growth and response functions are performed. Our observations suggest that the disease on prey population has a destabilizing or stabilizing effect depending on the level of force of infection and may act as a biological control for the persistence of the species.

scholarly journals Effects of Behavioral Tactics of Predators on Dynamics of a Predator-Prey System

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hui Zhang ◽  
Zhihui Ma ◽  
Gongnan Xie ◽  
Lukun Jia
Keyword(s):  
Time Scale ◽  
Stable State ◽  
Volterra Model ◽  
Fast Time ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Interaction ◽  
Game Dynamic

A predator-prey model incorporating individual behavior is presented, where the predator-prey interaction is described by a classical Lotka-Volterra model with self-limiting prey; predators can use the behavioral tactics of rock-paper-scissors to dispute a prey when they meet. The predator behavioral change is described by replicator equations, a game dynamic model at the fast time scale, whereas predator-prey interactions are assumed acting at a relatively slow time scale. Aggregation approach is applied to combine the two time scales into a single one. The analytical results show that predators have an equal probability to adopt three strategies at the stable state of the predator-prey interaction system. The diversification tactics taking by predator population benefits the survival of the predator population itself, more importantly, it also maintains the stability of the predator-prey system. Explicitly, immediate contest behavior of predators can promote density of the predator population and keep the preys at a lower density. However, a large cost of fighting will cause not only the density of predators to be lower but also preys to be higher, which may even lead to extinction of the predator populations.

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