[PDF] Top 20 The stability and bifurcation analysis of a discrete Holling Tanner model

... predator-prey model with Holling-Tanner functional response can give better predic- tion for some interacting ...The model also exhibits more complicated ...a discrete prey-predator ... See full document

... epidemic model in which the susceptible are assumed to satisfy the logistic equation will be taken up for detailed ...asymptotical stability of the disease-free equilibrium and endemic equilibrium will be ... See full document

... saddle-node bifurcation showing the co- existence of two stable equilibria separated by a saddle, whereby the fish population and the fishing effort varies with ...two bifurcation diagrams that show the ... See full document

... of model (3) exchanges its stability and occurs flip bi- ...continuous model corresponding to model (3) does not occur the bifurcation at the equilibrium E ∗ ...and stability of ... See full document

... epidemiological model with delay and media coverage is proposed and ...their stability are studied by using the theory of differential ...Hopf bifurcation about endemic equilibrium can occur under ... See full document

... In fact, we should note that there are delays in the infection process, including intra- cellular delay and CTLs immune response delay. We refer readers to [, ] and references therein. In [], Zhu and Zou studied a ... See full document

... epidemic model with nonlinear incidence rates is ...Hopf bifurcation occurs when these delays pass through a sequence of critical ...the stability and the direction of the Hopf bifurcation ... See full document

... a discrete predator–prey system with modified Holling–Tanner functional ...and bifurcation theory. Numerical simulations including bifurcation diagrams, maximum Lyapunov exponents, and ... See full document

... controlling bifurcation in a delayed fractional predator–prey system with incommensu- rate ...with Holling type-II functional ...dynamic analysis of a fractional-order delayed predator–prey system ... See full document

... the stability analysis of population ...local stability of a positive fixed point may be changed from stable to unstable or vice ...the bifurcation analysis of these systems with the ... See full document

... r increases. The bifurcation parameters are considered in the following two cases. Case 1: It can be observed from Fig. 1(a) that when r < 2.014, the equilibrium point is stable, when r > 2.014, it loses its ... See full document

... the fixed point (–2.149376214918635, 1.161532841710343) of map (3) will lose its stabil- ity, two fixed points could bifurcate from it, and eventually period-doubling phenomena occur. Bifurcation diagrams presented ... See full document

... This paper is organized as follows. In Section , we discuss the existence and stability of the positive fixed points for the system (.). In Section , we show that there exist some values of parameters such that ... See full document

... oscillator model with time delay is discretized by the Euler method. The discrete oscillator model is discussed by using Neimark-Sacker bifurcation ...the stability of the ... See full document

... the bifurcation theorem to prove the existence, stability, and direction of the Hopf bifurcation of a three-dimensional discrete-time SIRS epidemic ...two-dimensional discrete- time ... See full document

... the stability and bifurcation analysis, we are able to better understand the transition from a homeostatic state to oscillations triggered by a Hopf ...the bifurcation analysis, is in ... See full document

... predator-prey model has received more interest to investigate the dynamical behaviors between the ...response. Holling type II functional response is mostly used functional response among arthropod ... See full document

... A Holling-Tanner system with ratio-dependence functional response is revisited in this ...new analysis technique, two set of new conditions which ensure the global attractivity of the positive ... See full document

... predator–prey model with modified Holling– Tanner functional response under homogeneous Neumann boundary ...the stability of constant steady state for such ... See full document

... SIR model is one of the simplest and most fundamental of all epidemiological models and in these models with a single epidemic, births and deaths are ignored, and so, only two transitions are possible: infection ... See full document