Two-prey one-predator model

Elettreby, M. F.

doi:10.1016/j.chaos.2007.06.058

Cited by 54 publications

(33 citation statements)

References 12 publications

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“…Xu and Shao [20] showed the existence and global attractivity of positive periodic solutions for a Holling type II two-prey one-predator system. Stability analysis of a two-prey and one-predator model with group help and Holling type I response for predation was studied in [21,22]. Sharma and Samanta [23] developed a twoprey one-predator population model.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a food chain model consisting of two competitive preys and one predator

Ali¹,

Chakravarty

2015

Nonlinear Dyn

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The present article deals with the intraspecific competition among predator populations of a prey-dependent three-component food chain model system consisting of two competitive preys and one predator. The behaviour of the system near the biologically feasible equilibria is thoroughly analysed. 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 system experiences Hopf-Andronov bifurcation for suitable choice of parameters. The results of this investigation reveal that the intra-specific competition among predator populations can be beneficial for the survival of predator. The ecological implications of both the analytical and the numerical findings are discussed at length towards the end.

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Section: Introductionmentioning

confidence: 99%

Stability analysis of a food chain model consisting of two competitive preys and one predator

Ali¹,

Chakravarty

2015

Nonlinear Dyn

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“…Ahmed et al [16] have concentrated on the fractional-order predator-prey model and the fractional-order rabies model and studied the stability of equilibrium points. Elettreby [17] has proposed a new multiteam prey-predator model, in which the prey teams help each other. They observed that there is no help between the prey teams when predator is absent.…”

Section: Complexitymentioning

confidence: 99%

Research on a 3D Predator‐Prey Evolutionary System in Real Estate Market

Yang

Tang

2018

Complexity

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This paper establishes a model on the upstream and downstream relationship among private enterprises, provincial and local officials, and the central government in the real estate market using the population ecology theory of mutual relations among individual species from the perspective of business ecosystem. A dynamic model is introduced and the complex dynamical behaviors of such a predator-prey model are investigated by means of numerical simulation. The local stability conditions and complex dynamics are investigated, and the existence of chaos is discussed in the sense of Marotto theorem; bifurcation diagrams, Lyapunov exponents, sensitivity analysis for initial values, and time history figure of the system are mapped out and discussed. This shows that there are two routes to complicated dynamics, one of which is the cascade of flip bifurcations resulting in periodic cycles (and chaos), and the other one is Neimark-Sacker bifurcation which produces attractive invariant closed curves. We arrive at conclusions that the phenomenon of chaos is harmful to private enterprises, and unstable behavior is often unfavorable. Thus, linear feedback control is applied to drive the model to a stable state when the system exhibits chaotic behaviors, achieving the goal of eliminating the negative effects to a large extent.

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“…We prove this theorem by the method of average Lyapunov function. Let the average Lyapunov function for the system (1.2) be 22 2 y H 33 ; where H 11 ; H 22 and H 33 are all positive constants to be determined suitably in subsequent steps. Clearly, the function XðXÞ is a non negative continuous function defined in R 3 þ .…”

Section: ð5:5þmentioning

confidence: 99%

“…Further in most of the works on the dynamics of prey-predator system, the authors in general consider single predator depending on single prey. In ecosystem analysis through mathematical models, some authors have also considered two predator-single prey system (see, [14][15][16][17][18]) and few researchers have considered an ecosystem where one predator population depends on two or more prey populations (see [19][20][21][22]). It is also a common phenomenon to observe in some biological systems that a predator species depends on two different prey species.…”

Section: Introductionmentioning

confidence: 99%