Neimark-Sacker bifurcation and chaos control in Hassell-Varley model

Din, Qamar

doi:10.1080/10236198.2016.1277213

Cited by 53 publications

(22 citation statements)

References 29 publications

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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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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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“…In this section, we want to investigate the conditions for existence and direction of Neimark-Sacker bifurcation at positive equilibrium point of system (5). For a similar type of discussion related to the existence and direction of Neimark-Sacker bifurcation, we refer the interested reader to [1,23,24,28,[32][33][34][35][36][39][40][41] and references therein. Notice that, the roots of characteristic polynomial (16) are conjugate complex numbers if the following condition is satisfied:…”

Section: Neimark-sacker Bifurcationmentioning

confidence: 99%

“…In this section, we study two feedback control strategies in order to move the unstable trajectory towards the stable one. For similar types of investigations we refer to [1,[32][33][34][35][36][37][38][39][40][41] for controlling chaos in discrete-time population models. For some other applications related to chaos control, see also [51][52][53][54][55][56][57][58][59][60][61][62].…”

Section: Chaos Controlmentioning

confidence: 99%

“…In [1,[20][21][22][23][24], the parametric conditions for global behavior of host-parasitoid models are investigated. Recently, in [1,23,24,32,33,35], the parametric conditions for existence and direction of Neimark-Sacker bifurcation are investigated, and in [1,32,33,35] feedback chaos control strategies are implemented for controlling chaos and bifurcations in host-parasitoid models. Moreover, for state-feedback control design based on the matrix inequality approaches, we refer to [63][64][65][66].…”

Section: Introductionmentioning

confidence: 99%

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Controlling Chaos and Neimark–Sacker Bifurcation in a Host–Parasitoid Model

Din¹,

Hussain²

2018

Asian Journal of Control

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In this paper, a new density-dependent host-parasitoid model is proposed. The modification is based on density-dependent factor by introducing Hassell growth function in host population. Moreover, the permanence of solutions, existence and uniqueness of positive equilibrium, local asymptotic stability and global behavior of the positive equilibrium point are also investigated. It is demonstrated that system endures Neimark-Sacker bifurcation for wide range of bifurcation parameter. In order to control chaos due to emergence of Neimark-Sacker bifurcation, two feedback control strategies, that is, OGY and hybrid control methods are implemented. Finally, all mathematical analysis, particularly, Neimark-Sacker bifurcation, chaos control strategies, and global asymptotic stability of unique positive point are verified with the help of numerical simulations.

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“…In this section, we study the existence of Neimark-Sacker bifurcation for the positive steady-state .H , P / of system (3). Recently, many authors have discussed the existence of Neimark-Sacker bifurcation for discrete-time population models ( [15][16][17][18][19][20][21][22]). Various dynamical properties of a system can be discussed owing to emergence of Neimark-Sacker bifurcation.…”

Section: Neimark-sacker Bifurcationmentioning

confidence: 99%

Bifurcation analysis and chaos control in a host‐parasitoid model

Din¹,

Saeed

2017

Math Methods in App Sciences

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We investigate the qualitative behavior of a host‐parasitoid model with a strong Allee effect on the host. More precisely, we discuss the boundedness, existence and uniqueness of positive equilibrium, local asymptotic stability of positive equilibrium and existence of Neimark–Sacker bifurcation for the given system by using bifurcation theory. In order to control Neimark–Sacker bifurcation, we apply pole‐placement technique that is a modification of OGY method. Moreover, the hybrid control methodology is implemented in order to control Neimark–Sacker bifurcation. Numerical simulations are provided to illustrate theoretical discussion. Copyright © 2017 John Wiley & Sons, Ltd.

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Neimark-Sacker bifurcation and chaos control in Hassell-Varley model

Cited by 53 publications

References 29 publications

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

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

Controlling Chaos and Neimark–Sacker Bifurcation in a Host–Parasitoid Model

Bifurcation analysis and chaos control in a host‐parasitoid model

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