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

Tassaddiq, Asifa; Shabbir, Muhammad Sajjad; Din, Qamar; Ahmad, Khalid; Kazi, Sabeena

doi:10.1109/access.2020.3030778

Cited by 13 publications

(8 citation statements)

References 52 publications

(68 reference statements)

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“…Complexity Remark 3. Tassaddiq et al [35] used a nonstandard finite difference scheme and obtained the discrete ratio-dependent prey-predator model. ey showed that the considered system undergoes Neimark-Sacker bifurcation for larger values of the catchability coefficient.…”

Section: Case (I): Firstly Let Us Take the Parameter Values Asmentioning

confidence: 99%

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A Novel Discrete‐Time Leslie–Gower Model with the Impact of Allee Effect in Predator Population

Vinoth¹,

Sivasamy²,

Sathiyanathan³

et al. 2022

Complexity

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The discrete-time system has more complex and chaotic dynamical behaviors as compared to the continuous-time system. This paper extends a discrete Leslie–Gower predator-prey system with the Allee effect in the predator’s population, whose dynamics are analyzed and explored. We have determined the equilibrium points and studied their local stability properties. We find that the system undergoes flip bifurcation and Neimark–Sacker bifurcation around the interior equilibrium point by choosing the Allee parameter as a bifurcation parameter. We discuss the stability and direction of both bifurcations with the help of the normal form theory and center manifold theorem. The flip bifurcation and Neimark–Sacker bifurcation are the most common routes to the chaotic orbit in the discrete system. Moreover, we utilize state feedback, pole placement, and hybrid control methods to control the chaos in the system. The work is complete with the numerical simulations to confirm the analytical findings.

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Section: Case (I): Firstly Let Us Take the Parameter Values Asmentioning

confidence: 99%

“…Furthermore, the author implemented three different types of control strategies to control the chaos. Moreover, for some interesting results related to bifurcation and chaos control in the predator-prey models, we refer the readers to [33][34][35].…”

Section: Introductionmentioning

confidence: 99%

A Novel Discrete‐Time Leslie–Gower Model with the Impact of Allee Effect in Predator Population

Vinoth¹,

Sivasamy²,

Sathiyanathan³

et al. 2022

Complexity

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“…In this section, we implement the hybrid control method for controlling the chaos caused by the period-doubling bifurcation and for controlling the Neimark-Sacker bifurcation in (4). Such strategies have been discussed elsewhere in [21,[33][34][35][36][37]. We assume the following controlled system corresponding to model (4):…”

Section: Chaos Controlmentioning

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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“…Moreover, oscillations emerge from supercritical or subcritical Hop bifurcation distributions under relatively low costs for fear. Therefore, the effect of fear can create multi-stability in predator-prey systems [38][39][40]. Mondal et al [41] showed the saddle node distribution, Hopf bifurcation, and Bogdanov-Takens bifurcation in an imprecise predator-prey system to show the fear effect and the existence of nonlinear harvesting of predators in an uncertain environment [41].…”

Section: Introductionmentioning

confidence: 99%

Predator–Prey Interaction with Fear Effects: Stability, Bifurcation and Two-Parameter Analysis Incorporating Complex and Fractal Behavior

Din,

Naseem,

Shabbir

2024

Fractal Fract

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This study investigates the dynamics of predator–prey interactions with non-overlapping generations under the influence of fear effects, a crucial factor in ecological research. We propose a novel discrete-time model that addresses limitations of previous models by explicitly incorporating fear. Our primary question is: How does fear influence the stability of predator–prey populations and the potential for chaotic dynamics? We analyze the model to identify biologically relevant equilibria (fixed points) and determine the conditions for their stability. Bifurcation analysis reveals how changes in fear levels and predation rates can lead to population crashes (transcritical bifurcation) and complex population fluctuations (period-doubling and Neimark–Sacker bifurcations). Furthermore, we explore the potential for controlling chaotic behavior using established methods. Finally, two-parameter analysis employing Lyapunov exponents, spectrum, and Kaplan–Yorke dimension quantifies the chaotic dynamics of the proposed system across a range of fear and predation levels. Numerical simulations support the theoretical findings. This study offers valuable insights into the impact of fear on predator–prey dynamics and paves the way for further exploration of chaos control in ecological models.

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

Cited by 13 publications

References 52 publications

A Novel Discrete‐Time Leslie–Gower Model with the Impact of Allee Effect in Predator Population

A Novel Discrete‐Time Leslie–Gower Model with the Impact of Allee Effect in Predator Population

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

Predator–Prey Interaction with Fear Effects: Stability, Bifurcation and Two-Parameter Analysis Incorporating Complex and Fractal Behavior

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