Dynamical Complexity in a Class of Novel Discrete-Time Predator-Prey Interaction With Cannibalism

Shabbir, Muhammad Sajjad; Din, Qamar; Alabdan, Rana; Tassaddiq, Asifa; Ahmad, Khalid

doi:10.1109/access.2020.2995679

Cited by 19 publications

(8 citation statements)

References 45 publications

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“…In this section, our aim is to apply two chaos control methods to system (3). These chaos control methods have been most frequently used strategies for controlling bifurcating and chaotic behaviors of discrete-time models [11], [12], [17], [29]- [32], [42], [46], [48], [49]. The first chaos control method which is known as Ott-Grebogi-Yorke (OGY) [57] method is considered as pioneer control method for discrete models with some drawbacks [58].…”

Section: Chaos Controlmentioning

confidence: 99%

“…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%

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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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Section: Chaos Controlmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Din¹,

Rafaqat

Elsadany

et al. 2020

IEEE Access

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“…By contrast, a recent study led to the discrete dynamical system becoming more suitable than a continuous version when the population is non-overlapping (e.g., see, Jing et al [14], Liu et al [15], Lopez-Ruiz and Fournier-Prunaret [16], Neubert and Kot [17]). Furthermore, multiple existing studies related to the dynamics of predator-prey models are described in [18][19][20][21][22][23][24][25][26]. In [27], the Holling type-III functional response was introduced in both populations (prey and predator).…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, a detailed investigation of some charismatic population models and their qualitative behavior are provided (see, Din and Din et al [18][19][20][21][22][23][24][25][26] and the references therein).…”

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confidence: 99%

Discretization, Bifurcation, and Control for a Class of Predator-Prey Interactions

et al. 2022

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The present study focuses on the dynamical aspects of a discrete-time Leslie–Gower predator–prey model accompanied by a Holling type III functional response. Discretization is conducted by applying a piecewise constant argument method of differential equations. Moreover, boundedness, existence, uniqueness, and a local stability analysis of biologically feasible equilibria were investigated. By implementing the center manifold theorem and bifurcation theory, our study reveals that the given system undergoes period-doubling and Neimark–Sacker bifurcation around the interior equilibrium point. By contrast, chaotic attractors ensure chaos. To avoid these unpredictable situations, we establish a feedback-control strategy to control the chaos created under the influence of bifurcation. The fractal dimensions of the proposed model are calculated. The maximum Lyapunov exponents and phase portraits are depicted to further confirm the complexity and chaotic behavior. Finally, numerical simulations are presented to confirm the theoretical and analytical findings.

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“…NEIMARK-SACKER BIFURCATIONIn this section, we investigate the existence criteria of NSB around unique positive equilibrium Ρ 2 by considering consumption ability of prey which is ′ ′ as bifurcation parameter. For detail analysis of bifurcation in discrete-time population models, we refer to the work done by the authors[14][15][16][17]. Obviously, when Neimark-Sacker bifurcation exists then as a result, dynamically closed curves are appearing and attracting steady-states are unstable as varied parameter move towards the bifurcation parameter.…”

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confidence: 99%

A Ratio-Dependent Nonlinear Predator-Prey Model With Certain Dynamical Results

et al. 2020

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In order to see the dynamics of prey-predator interaction, differential or difference equations are frequently used for modeling of such interactions. In present manuscript, we explore some qualitative aspects of two-dimensional ratio-dependent predator-prey model. Taking into account the non-overlapping generations for class of predator-prey system, a novel consistency preserving scheme is proposed. Our study reveals that the implemented discretization is bifurcation preserving. Some dynamical aspects including local behavior of equilibria, phase-plane analysis and emergence of Hopf bifurcation for continuous predator-prey model are studied. Moreover, existence of biologically feasible fixed points, their local asymptotic behavior and phase-plane classification of interior (positive) fixed point are carried out. Furthermore, bifurcation theory of normal forms is implemented to prove that proposed discrete-time model undergoes Neimark-Sacker bifurcation around its unique positive fixed point. Taking into account the bifurcating and fluctuating behaviour of discrete system, three chaos control strategies are implemented. Numerical simulations are provided to illustrate the theoretical discussion and effectiveness of introduced chaos control methods. INDEX TERMS Prey-predator interaction; stability analysis; Neimark-Sacker bifurcation; chaos control.

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Dynamical Complexity in a Class of Novel Discrete-Time Predator-Prey Interaction With Cannibalism

Cited by 19 publications

References 45 publications

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

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

Discretization, Bifurcation, and Control for a Class of Predator-Prey Interactions

A Ratio-Dependent Nonlinear Predator-Prey Model With Certain Dynamical Results

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