Complexity and chaos control in a discrete-time prey-predator model

Din, Qamar

doi:10.1016/j.cnsns.2017.01.025

Cited by 184 publications

(99 citation statements)

References 31 publications

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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%

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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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Section: Neimark-sacker Bifurcationmentioning

confidence: 99%

Section: Chaos Controlmentioning

confidence: 99%

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

Din¹,

Hussain²

2018

Asian Journal of Control

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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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“…If one may wish to alter the positions of positive equilibrium and to obtain its stability, to achieve the aim, one of the techniques used is to alter system structurally by introducing "indirect control" variables. Though there are many works on the single species or multispecies competition systems with feedback controls [12][13][14][15][16]. To the best of the authors' knowledge, there are still no scholars who are investigating the stability property of the 2D spatially discrete reactiondiffusion competitive system with feedback controls; this motivates us to propose such a model as follows:…”

Section: Introductionmentioning

confidence: 99%

Feedback Control and Parameter Invasion for a Discrete Competitive Lotka–Volterra System

Lou

et al. 2018

Discrete Dynamics in Nature and Society

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State feedback is used to stabilize the Turing instability at the unstable equilibrium point of a discrete competitive Lotka-Volterra system. In addition, a regularization method is applied to parameter inversion for the given Turing system and numerical simulation can verify the effectiveness of the algorithm. Furthermore, how less or more sample data and dependence on the initial state affect estimation procedure are tested.

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Complexity and chaos control in a discrete-time prey-predator model

Cited by 184 publications

References 31 publications

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

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

Bifurcation analysis and chaos control in a host‐parasitoid model

Feedback Control and Parameter Invasion for a Discrete Competitive Lotka–Volterra System

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