We consider a discrete-time predator-prey system with Holling type I functional response and Gomp... more We consider a discrete-time predator-prey system with Holling type I functional response and Gompertz growth of prey population to study its dynamic behaviors. We algebraically show that the predator-prey system undergoes a flip bifurcation (FB) and Neimark-Sacker bifurcation (NSB) in the interior of when one of the model parameter crosses its threshold value. We determine the existence conditions and direction of bifurcations by using the center manifold theorem and bifurcation theorems. We present numerical simulations to illustrate theoretical results which include the bifurcation diagrams, phase portraits, appearing or disappearing closed curves, periodic orbits, and attracting chaotic sets. In order to justify the existence of chaos in the system, maximum Lyapunov exponents (MLEs) and fractal dimension (FD) are computed numerically. Finally, chaotic trajectories have been controlled by applying feedback control method.
The dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holli... more The dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holling type IV functional response is examined. We algebraically show that the system undergoes a bifurcation (flip or Neimark-Sacker) in the interior of R 2 +. Numerical simulations are presented not only to validate analytical results but also to show chaotic behaviors which include bifurcations, phase portraits, period 2, 4, 6, 8, 10, and 20 orbits, invariant closed cycle, and attracting chaotic sets. Furthermore, we compute numerically maximum Lyapunov exponents and fractal dimension to justify the chaotic behaviors of the system. Finally, a strategy of feedback control is applied to stabilize chaos existing in the system.
We consider a discrete-time predator-prey system with Holling type I functional response and Gomp... more We consider a discrete-time predator-prey system with Holling type I functional response and Gompertz growth of prey population to study its dynamic behaviors. We algebraically show that the predator-prey system undergoes a flip bifurcation (FB) and Neimark-Sacker bifurcation (NSB) in the interior of when one of the model parameter crosses its threshold value. We determine the existence conditions and direction of bifurcations by using the center manifold theorem and bifurcation theorems. We present numerical simulations to illustrate theoretical results which include the bifurcation diagrams, phase portraits, appearing or disappearing closed curves, periodic orbits, and attracting chaotic sets. In order to justify the existence of chaos in the system, maximum Lyapunov exponents (MLEs) and fractal dimension (FD) are computed numerically. Finally, chaotic trajectories have been controlled by applying feedback control method.
The dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holli... more The dynamic behavior of a discrete-time predator-prey system of Leslie type with simplified Holling type IV functional response is examined. We algebraically show that the system undergoes a bifurcation (flip or Neimark-Sacker) in the interior of R 2 +. Numerical simulations are presented not only to validate analytical results but also to show chaotic behaviors which include bifurcations, phase portraits, period 2, 4, 6, 8, 10, and 20 orbits, invariant closed cycle, and attracting chaotic sets. Furthermore, we compute numerically maximum Lyapunov exponents and fractal dimension to justify the chaotic behaviors of the system. Finally, a strategy of feedback control is applied to stabilize chaos existing in the system.
Uploads
Papers by Sarker RANA