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

Ma, Xiaohua; Din, Qamar; Rafaqat, Muhammad; Javaid, Nasir; Feng, Yongliang

doi:10.3390/math8040536

Cited by 12 publications

(9 citation statements)

References 53 publications

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“…where α ∈]0, 1[ denotes external control parameter for system (31). On the other hand, the Jacobian matrix for (31) at…”

Section: Chaos Controlmentioning

confidence: 99%

“…Furthermore, the following Lemma gives parametric conditions for local stability of fixed point (x * , y * ) = 1 c , ac−b c for the controlled system (31).…”

Section: Chaos Controlmentioning

confidence: 99%

“…For similar type of investigations related to discrete versions of predator-prey systems, we refer to [24]- [30] and references therein. Recently, Ma et al [31] studied stability, bifurcation and chaos control for a host-parasitoid system with a Beverton-Holt growth function for a host population and Hassell-Varley framework. Shabbir et al [32] proposed a new class of prey-predator interaction for non-overlapping generations with implementation of cannibalism in prey population.…”

Section: Introductionmentioning

confidence: 99%

“…The positive equilibrium (x * , y * ) = 1 c , ac−b c of the controlled system(31) is locally asymptotically stable if and only if the following condition holds true:In this section, some interesting numerical simulations related to system (3) are presented for particular choice of parametric values. These numerical results give evidence of flip bifurcation, Hopf bifurcation for system (3) at its positive steady-state, and show effectiveness of chaos control strategies.…”

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confidence: 99%

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Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model

Din¹,

Rafaqat

Elsadany

et al. 2020

IEEE Access

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Bifurcation theory (center manifold and Ljapunov-Schmidt reduction, normal form theory, universal unfolding, calculation of bifurcation diagrams) has become an important and very useful means in the solution of nonlinear stability problems in many branches of engineering. The present study deals with qualitative behavior of a two-dimensional discrete-time system for interaction between prey and predator. The discrete-time model has more chaotic and rich dynamical behavior as compare to its continuous counterpart. We investigate the qualitative behavior of a discrete-time Lotka-Volterra model with linear functional response for prey. The local asymptotic behavior of equilibria is discussed for discrete-time Lotka-Volterra model. Furthermore, with the help of bifurcation theory and center manifold theorem, explicit parametric conditions for directions and existence of flip and Hopf bifurcations are investigated. Moreover, two chaos control methods, that is, OGY feedback control and hybrid control strategy, are implemented. Numerical simulations are provided to illustrate theoretical discussion and their effectiveness. INDEX TERMS Lotka-Volterra model, stability, flip bifurcation, Hopf bifurcation, chaos control.

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“…where α ∈]0, 1[ denotes external control parameter for system (31). On the other hand, the Jacobian matrix for (31) at…”

Section: Chaos Controlmentioning

confidence: 99%

“…Furthermore, the following Lemma gives parametric conditions for local stability of fixed point (x * , y * ) = 1 c , ac−b c for the controlled system (31).…”

Section: Chaos Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model

Din¹,

Rafaqat

Elsadany

et al. 2020

IEEE Access

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“…Also, we have investigated the stability at positive fixed point, bifurcation analysis, and chaos control. A lot of work done by many researchers have been cited by Peng et al (2017), Chen et al (2013), Cheng and Cao (2016), Ishaque et al (2019), Din (2019), Ma et al (2020), and Din and Ishaque (2020). To do so, we use the discrete-time form in case of non-overlapping generations with comprehensive theoretical discussions.…”

Section: Introductionmentioning

confidence: 99%

Mutual interference and its effects on searching efficiency between predator–prey interaction with bifurcation analysis and chaos control

Ishaque

Din²,

Taj

2021

Journal of Vibration and Control

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In this paper, we study the dynamic of the predator–prey model based on mutual interference and its effects on searching efficiency. The parametric conditions, existence, and stability for trivial and boundary equilibrium points are studied. Also, it has shown that by applying the center manifold theorem and bifurcation theory, system undergoes Neimark–Sacker bifurcation across the neighborhood of a positive fixed point. Moreover, due to the bifurcation and chaos which objectively exist in a system, three chaos control strategies are designed and used. Moreover, to validate our theoretical and analytical discussions, numerical simulations are applied to show complex and chaotic behavior. Finally, theoretical discussions are validated with experimental field data.

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