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Effect of prey refuge on the dynamics and equilibrium density of
Predator-prey models Stability Limit cycles Prey refuge
2011/10/20
In this paper, we use an analytical approach to study the dynamics of the simplest forms of refuge using by prey. Here we incorporate prey refuge in a widely known continuous model|the Lotka-Volterra ...
A Lotka-Volterra model with impulsive effects on the prey and stage structure on the predator
Stage structure Impulsive Global attractivity Permanence
2010/9/21
In this paper, we consider a Lotka-Volterra model with impulsive effects on the prey and stage structure on the predator. We prove that all solutions of the system are uniformly ultimately bounded, su...
Nonconstant predator harvesting on ratio-dependent predator-prey models
Predator-prey models harvesting dynamical systems
2010/9/21
The dynamics of a ratio-dependent predator-prey model with two different non-constant harvesting functions depending on the predator population is studied. Equilibria and periodic orbits are computed ...
Permanence and periodic solution for a predator-prey model with mixed-type functional response
Predator-prey model mixed-type functional response
2010/9/14
In this paper, a predator-prey model with mixed-type functional response is investigated. Sufficient conditions are derived that guarantee the permanence of the system. Meanwhile, when the system is p...
The chaos and control of a prey-predator model with some unknown parameters
Dynamic estimators Attractors Unknown parameters
2010/9/14
In this paper we study the problems of chaos and control of the prey-predator model with some unknown parameters. We will use the non-linear feedback control approach to stabilize this system about it...
A global mathematical investigation of a predator-prey model
predator-prey plane differential system
2010/4/8
We construct a global bifurcation diagram of the plane differential system $$ {l} \dot x = x(1-x)-x y/(a+x^2), \dot y = y(\delta-\beta y/x), x(t)>0, y(t)>0, a>0, \delta>0, \beta>0, $$ which describes ...
Periodic solutions for a predator-prey system with dispersal and semi-ratio-dependent functional response
functional response periodic solution dispersal coincidence
2010/9/10
By using a continuation theorem of Mawhin’s coincidence degree , studied a periodic predator-prey system with dispersal and semi-ratiofunctional response, sufficient conditions are obtained for the ex...
Qualitative analysis for a prey-mesopredator-superpredator model
global existence steady state solutions stability prey mesopredator
2010/9/14
In this paper we consider a reaction-diffusion model with three species arising in the context of ecology. We investigate the global existence, coexistence and the stability of the positive steady sta...
A stage-structure predator-prey model with functional response
immature mature functional response Hamiltonian
2010/9/10
In this paper, a class of two species predator-prey model with functional response and harvesting, we consider a stage-structured population model with two life stages, immature and mature; and assume...
Existence of Limit Cycles in a Predator-Prey System With a Functional Response of the Form Arctan(ax)
Predator prey system limit cycle unctional response
2008/11/25
We consider a predator prey system with the functional response of the form
µ(x) = arctan(ax); a > 0. The main concern in this paper is the existence of
limit cycles for such system. A necessa...
Stability of limit cycle in a predator-prey model with modified Leslie-Gower and Holling-type II schemes with time delay
Delay differential equations stability/unstability
2010/9/14
In this paper we study the stability of the periodic solutions of a model set forth by M. A. Aziz Alaoui et al. [1, 11] with time delay, which describes the competition between the predator and prey. ...
THE EXTINCTION IN NONAUTONOMOUS PREY-PREDATORLOTKA-VOLTERRA SYSTEMS
Nonautonomous Lotka-Volterra
2007/12/11
In this paper some new criteria about the extinction of solutions for two dimensional nonautonomous prey-predator Lotka-Volterra systems are established. The criteria obtained improve the results by G...
The Dynamics of a Predator-prey Model with Ivlev's Functional Response Concerning Integrated Pest Management
IPM strategy Ivlev's functional response Impulsive effect Extinction Permanence
2007/12/11
A mathematical model of a predator-prey model withIvlev's functional response concerning integrated pest management(IPM) is proposed and analyzed. We show that there exists a stablepest-eradication pe...
On the PredatorPrey System with Holling-$(n+1)$ Functional Response
Predator--prey system Limit cycle Uniqueness Dulac function
2007/12/11
The qualitative properties of a predator{prey system with Holling-(n + 1) functional response and a fairly general growth rate are completely investigated. The necessary and sufficient condition to gu...
Analyses of Bifurcations and Stability in a Predator-prey System
Predator-prey system Limit cycle Bogdanov-Takens bifurcation
2007/12/11
In this paper the dynamical behaviors of apredator-prey system with Holling Type-IV functional response are investigated in detail by using the analyses of qualitative method, bifurcation theory,...