The Dynamical Analysis of a Prey-Predator Model with a Refuge-Stage Structure Prey Population (original) (raw)
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In this paper, a food web model consisting of two predator-one stage structured prey involving Lotka-Voltera type of functional response and a prey refuge , is proposed and analyzed. It is assumed that the prey growth logistically in the absence of predator. The role of prey refuges in predator-prey model is investigated. The existence , uniqueness and boundedness of the solution are studied. The existence and the stability analysis of all possible equilibrium points are studied. Suitable Lyapunov functions are used to study the global dynamics of the proposed model. Numerical simulation for different sets of parameter value and for different sets of initial conditions are carried out to investigate the influence of parameters on the dynamical behavior of the model and to support the obtained analytical results of the model .
STABILITY ANALYSIS OF STAGE-STRUCTURED PREY MODEL INCORPORATING A PREY REFUGE
In this paper, a food chain model consisting of mid- predator and top predator-stage structured prey involving two functional response Lotka-Voltera type and Holling type-II with a prey refuge, is proposed and analyzed. For this model, it is assumed that the prey growth logistically in the absence of predator. The role of prey refuges in predator-prey model is investigated. The existence, uniqueness and boundedness of the solution of this model are studied. The stability analysis of all possible equilibrium points are studied.Suitable Lyapunov functions are used to study the global dynamics of the proposed model.Finally, numerical simulation for different sets of parameter value and for different sets of initial conditions are carried out to investigate the influence of parameters on the dynamical behavior of the model and to support our obtained analytical results of the model. Keywords: food chain, Lyapunov function, refuge, stability analysis, stage-structure. Keywords: food chain, Lyapunov function, refuge , stability analysis , stage-structure .
The Influence of Stage Structure and Prey Refuge on the Stability of the Predator-Prey Model
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This paper aims to study the prey refuge impact on the dynamic behaviour of a stage structure predator-prey model. The model consists of four ecological species: prey in the protected and unprotected area and immature and mature predators. It assumes the grown predator can feeds only on the prey in an unreserved area. The conditions that guarantee the existence of the possible fixed points are found. Further, the local stability around all of the equilibria is considered. Then, using the Lyapunov direct method, the essential conditions for the global stability of the equilibria are adopted. Numerical simulations are illustrated to confirm our results. It concluded that the protected area positively affects the system's coexistence.
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In this paper, we established the condition of the occurrence of local bifurcation (such as saddle-node, transcritical and pitchfork)with particular emphasis on the hopf bifurcation near of the positive equilibrium point of ecological mathematical model consisting of prey-predator model involving prey refuge with two different function response are established. After the study and analysis, of the observed incidence transcritical bifurcation near equilibrium point 𝐸0,𝐸1,𝐸2 as well as the occurrence of saddle-node bifurcation at equilibrium point 𝐸3.It is worth mentioning, there are no possibility occurrence of the pitch fork bifurcation at each point. Finally, some numerical simulation are used to illustration the occurrence of local bifurcation o this model
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A prey-predator model incorporating prey refuge with variable carrying capacity and Holling type-II functional response is proposed and analyzed. The model includes a case of increasing carrying capacity as well as a decreasing carrying capacity case. Sufficient conditions are derived to ensure the existence and local stability of the equilibrium points of the proposed model. Moreover, the occurrence of transcritical bifurcation as well as Hopf bifurcation are investigated. The effect of some model parameter related to the prey refuge and the variable carrying capacity on the prey-predator dynamics has been examined. Numerical simulations are presented to demonstrate the theoretical results and to illustrate the effect of these parameters on the model dynamics. Moreover, a comparison with the constant carrying case has been presented.
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The present article deals with a constant proportion of prey refuge in presence of both the inter specific competition and the intra-specific competition among predator populations of a prey-dependent three component food chain model consisting of two competitive predators sharing one prey species as their food. The behaviour of the system near the biologically feasible equilibria is thoroughly analyzed. Boundedness and dissipativeness of the system are established. The stability analysis including local and global stability of the equilibria has been carried out in order to examine the behaviour of the system. The present model system experiences Hopf-Andronov bifurcation for suitable choice of the parameter values. The influences of the prey refuge parameters on the dynamical behaviour of the system are exhibited through several plots and discussed at some equilibrium positions. It is worthnoting that prey refuge has stabilization effect in some selected situations which may be of some use for biological control. Numerical simulations are performed to illustrate and to support the analytical findings so as to validate the applicability of the model under consideration.
Dynamics and Numerical Simulation of Stage Structure Prey-Predator Models
Proceedings of the International Conference on Science and Technology (ICST 2018), 2018
In the present paper, we studied a prey-predator model with stage-structure for prey. Prey populations which are divided into subpopulations, one is immature prey and the other is mature prey. We investigate the stability of prey-predator models as well as local analysis of four equilibrium obtained and analyzed how the dynamical behavior if the solution is stable or unstable. Numerical simulations are performed from the system around the equilibrium point to show dynamic behavior around that point with several different conditions andinitial values.
A FOOD CHAIN STRUCTURES AND DYNAMICS ACROSS A REFUGE STAGE-STRUCTURE PREY- PREDATOR MODEL
In the present paper the structures and dynamics of a food chain prey- predator model are proposed and studied. The two stages and refuge in prey and two predators (top and mid) are considered. Different types of functional responses have been proposed. The conditions, which guarantee the existence of equilibrium points, have been investigated. Uniqueness and boundedness of the solution of the system are proven. The local and global dynamical behaviors are discussed and analyzed. Finally, numerical simulations are carried out not only to confirm the theoretical results obtained, but also to show the effects of the refuge and the variation of each parameter on our proposed system.
Dynamics of a Stage-Structured Predator-Prey Model
International Journal of Applied Physics and Mathematics, 2017
This paper deals with the dynamics of a stage-structured predator-prey system. The immature and mature prey are predated by the predator for which modified Holling type II functional response is considered in the model. The solution of the system is positive and bounded. Stability analysis has been discussed about all possible feasible equilibrium points. The origin and boundary equilibrium points are shown to be globally asymptotically stable. The parameters are identified for which system also admits trans-critical bifurcation about these points. The occurrence of Hopf bifurcation has been shown through numerical simulation about positive interior point. Persistence condition is obtained.