[PDF] Top 20 Discrete time bifurcation behavior of a prey predator system with generalized predator

... flip bifurcation, numerical simulations display orbits of period 2, 4, 8 and chaotic sets; whereas in the case of a Neimark-Sacker bifurcation, a smooth invariant circle bifurcates from the fixed point and ... See full document

... Moreover, the remaining discussion for this paper is organized as follows. In Sect. 2, we explore the existence of equilibria and conditions for their local asymptotic stability. In Sect. 3, an explicit criterion for ... See full document

... lation for the positive fixed point of system (), the Neimark-Sacker bifurcation emerges from the fixed point (, ) at r = . From Figure (a) and (b), we observe that the fixed point of map () is stable ... See full document

... of time or ...asymptotic behavior of solution in logistic models with feedback controls, in which the control variables satisfy certain differential ... See full document

... a discrete-time economic predator– prey system in the presence of a type of nonlinear harvesting ...the discrete model compared with the continuous one proposed in [9], in- ... See full document

... of predator-prey models, which include bifurcations and chaos phenomena for the discrete-time ...flip bifurcation and Hopf bifurcation by using the center manifold theorem and ... See full document

... a discrete-time prey–predator model with Allee effect on the prey population are ...Neimark–Sacker bifurcation at the unique positive fixed point by choosing a as a ... See full document

... studied predator–prey dynamic models and developed them in many ways ...stochastic prey–predator system in a polluted environment with Beddington–DeAngelis functional response and ... See full document

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

... Conclusion In this paper, we considered a three-stage-structured prey-predator system with discrete and continuous time delays and analyzed the stability of the boundary and positive equ[r] ... See full document

... new bifurcation diagrams is obtained as plotted in ...the predator-prey system (3) expe- riences Neimark-Sacker bifurcation and flip bifurcation both together when parameter a ... See full document

... same time every ...by discrete-time (difference equations) model than continuous equations (Hu et ...the discrete dynamics of the one-dimensional logistic map can produce a much richer set of ... See full document

... Lotka-Volterra predator-prey model [, ] is one of the most important population ...other predator-prey models of vari- ous types that have been extensively investigated, and some of the ... See full document

... The prey-predator model is an area of great interest for many ecologists and ...dynamical behavior of the prey-predator system in ecology and contributed to the growth of ... See full document

... dynamical behavior of a discrete prey-predator system with three ...simulations. Time series plots and phase portraits are obtained for different sets of parameter ...values. ... See full document

... important Predator – Prey models with the functional response is the Holling type – IV, originally due to Holling which has been extensively studies in many articles [4-6, ...of predator to its ... See full document

... between predator and prey ...dynamical behavior such as the period-2, -4, -11, -13, -15 and -22 ...the discrete-time ...the discrete-time ... See full document

... In the biological field, the study of the stability and bifurcations of the reaction-diffusion models describing a variety of biological phenomena is one of the fundamental problems, which can be conducive to understand ... See full document

... stage-structured predator-prey systems has attracted considerable attention in recent years see 1–6 and the reference ...following predator-prey model with stage structure for predator, ... See full document

... To rationally develop the exploitation of biological resources, many scholars have con- sidered predator–prey models with harvesting. The harvesting can be mainly divided into three types: (i) constant ... See full document