Stability, bifurcation analysis and chaos control for a predator-prey system

Din, Qamar

doi:10.1177/1077546318790871

Cited by 48 publications

(33 citation statements)

References 49 publications

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“…On the other hand, chaos control methods are widely used in almost all branches of applied science [37]. For further details related to chaos control methods in discrete-time systems, we refer to [38][39][40][41][42][43][44][45][46][47][48].…”

Section: Chaos and Bifurcation Controlmentioning

confidence: 99%

A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control

Ma¹,

Din

Rafaqat

et al. 2020

Mathematics

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The aim of this article is to study the qualitative behavior of a host-parasitoid system with a Beverton-Holt growth function for a host population and Hassell-Varley framework. Furthermore, the existence and uniqueness of a positive fixed point, permanence of solutions, local asymptotic stability of a positive fixed point and its global stability are investigated. On the other hand, it is demonstrated that the model endures Hopf bifurcation about its positive steady-state when the growth rate of the consumer is selected as a bifurcation parameter. Bifurcating and chaotic behaviors are controlled through the implementation of chaos control strategies. In the end, all mathematical discussion, especially Hopf bifurcation, methods related to the control of chaos and global asymptotic stability for a positive steady-state, is supported with suitable numerical simulations.

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Section: Chaos and Bifurcation Controlmentioning

confidence: 99%

A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control

Ma¹,

Din

Rafaqat

et al. 2020

Mathematics

Self Cite

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“…On the other hand, population models with non-overlapping generations have more irregular complex behaviour. For some recent investigation related to chaos control in discrete-time models we refer to [1,[13][14][15][16][17][18][19][20][22][23][24] and references are therein. In this section, first we discuss pole-placement chaos control method based on state feedback control which was introduced by Romeiras et al [44] (also see [41]).…”

Section: Chaos Controlmentioning

confidence: 99%

Bifurcation analysis and chaos control for a plant–herbivore model with weak predator functional response

Din¹,

Shabbir

Ahmad

2019

Journal of Biological Dynamics

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The interaction between plants and herbivores is one of the most fundamental processes in ecology. Discrete-time models are frequently used for describing the dynamics of plants and herbivores interaction with non-overlapping generations, such that a new generation replaces the old at regular time intervals. Keeping in view the interaction of the apple twig borer and the grape vine, the qualitative behaviour of a discrete-time plant-herbivore model is investigated with weak predator functional response. The topological classification of equilibria is investigated. It is proved that the boundary equilibrium undergoes transcritical bifurcation, whereas unique positive steady-state of discrete-time plant-herbivore model undergoes Neimark-Sacker bifurcation. Numerical simulation is provided to strengthen our theoretical discussion. ARTICLE HISTORY

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“…Furthermore, the implementation for such a hybrid control strategy is comparatively simple one and it is based on both parameter perturbation and state feedback control strategy. It is worthwhile to mention some other investigations for controlling chaos in discrete-time systems and the interested reader is referred to [22][23][24][25][26][27][28][29][30][31].…”

Section: Chaos Controlmentioning

confidence: 99%

Bifurcation and chaos control in a discrete-time predator–prey model with nonlinear saturated incidence rate and parasite interaction

et al. 2019

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The dynamical behavior of the predator-prey system is influenced effectively due to the mutual interaction of parasites. Regulations are imposed on biodiversity due to such type of interaction. With implementation of nonlinear saturated incidence rate and piecewise constant argument method of differential equations, a three-dimensional discrete-time model of prey-predator-parasite type is studied. The existence of equilibria and the local asymptotic stability of these steady states are investigated. Moreover, explicit criteria for a Neimark-Sacker bifurcation and a period-doubling bifurcation are implemented at positive equilibrium point of the discrete-time model. Chaos control is discussed through implementation of a hybrid control technique based on both parameter perturbation and a state feedback strategy. At the end, some numerical simulations are provided to illustrate our theoretical discussion.

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Stability, bifurcation analysis and chaos control for a predator-prey system

Cited by 48 publications

References 49 publications

A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control

A Density-Dependent Host-Parasitoid Model with Stability, Bifurcation and Chaos Control

Bifurcation analysis and chaos control for a plant–herbivore model with weak predator functional response

Bifurcation and chaos control in a discrete-time predator–prey model with nonlinear saturated incidence rate and parasite interaction

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