Qualitative analysis and phase of chaos control of the predator-prey model with Holling type-III

AL-Kaff, Mohammed O.; El-Metwally, H.; Elabbasy, Elmetwally M.

doi:10.1038/s41598-022-23074-3

Cited by 5 publications

(2 citation statements)

References 28 publications

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“…Regulating chaotic dynamics towards a periodic orbit or a fixed point is necessary to improve system performance. We applied the feedback control method known as OGY, as documented in the literature [27,28], to model (4). The basic aim is to make small, time-dependent linear perturbations to the control parameter α in order to nudge the state towards the stable manifold of the desired fixed point, thus controlling the chaos resulting from the NB and PB at the fixed point of model ( 4).…”

Section: Control Of Chaosmentioning

confidence: 99%

Dynamic Behavior and Bifurcation Analysis of a Modified Reduced Lorenz Model

Al-Kaff,

AlNemer,

El-Metwally

et al. 2024

Mathematics

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This study introduces a newly modified Lorenz model capable of demonstrating bifurcation within a specified range of parameters. The model demonstrates various bifurcation behaviors, which are depicted as distinct structures in the diagram. The study aims to discover and analyze the existence and stability of fixed points in the model. To achieve this, the center manifold theorem and bifurcation theory are employed to identify the requirements for pitchfork bifurcation, period-doubling bifurcation, and Neimark–Sacker bifurcation. In addition to theoretical findings, numerical simulations, including bifurcation diagrams, phase pictures, and maximum Lyapunov exponents, showcase the nuanced, complex, and diverse dynamics. Finally, the study applies the Ott–Grebogi–Yorke (OGY) method to control the chaos observed in the reduced modified Lorenz model.

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Section: Control Of Chaosmentioning

confidence: 99%

Dynamic Behavior and Bifurcation Analysis of a Modified Reduced Lorenz Model

Al-Kaff,

AlNemer,

El-Metwally

et al. 2024

Mathematics

Self Cite

View full text Add to dashboard Cite

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“…( 27,[29][30][31][32]). Assume that the polynomial K(ω) = ω 2 − pω + q, where P (1) > 0, and ω 1 and ω 2 are the two roots of K(ω) = 0.…”

Section: Local Stability Of Equilibrium Pointmentioning

confidence: 99%

Bifurcation Analysis and Chaos Control for Prey-Predator Model With Allee Effect

Almatrafi,

Berkal

2023

Int. J. Anal. Appl.

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The main purpose of this work is to discuss the dynamics of a predator-prey dynamical system with Allee effect. The conformable fractional derivative is applied to convert the fractional derivatives which appear in the governing model into ordinary derivatives. We use the piecewise-constant approximation method to discritize the considered model. We also investigate the occurrence of positive equilibrium points. Moreover, we analyse the stability of the equilibrium point using some stability theorems. This work also explores a Neimark-Sacker bifurcation and a period-doubling bifurcation using the theory of bifurcations. The distance between the obtained equilibrium point and some closed curves is examined for various values for the considered bifurcation parameter. The chaos control is nicely analysed using the hybrid control approach. Furthermore, we present the maximum Lyapunov exponents for different values for the bifurcation parameter. Numerical simulations are utilized to ensure that the obtained theoretical results are correct. The used techniques can be applied to deal with predator-prey models in various versions.

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Exploring chaos and bifurcation in a discrete prey–predator based on coupled logistic map

Al-Kaff,

El-Metwally,

Elsadany

et al. 2024

Sci Rep

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This research paper investigates discrete predator-prey dynamics with two logistic maps. The study extensively examines various aspects of the system’s behavior. Firstly, it thoroughly investigates the existence and stability of fixed points within the system. We explores the emergence of transcritical bifurcations, period-doubling bifurcations, and Neimark-Sacker bifurcations that arise from coexisting positive fixed points. By employing central bifurcation theory and bifurcation theory techniques. Chaotic behavior is analyzed using Marotto’s approach. The OGY feedback control method is implemented to control chaos. Theoretical findings are validated through numerical simulations.

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Qualitative analysis and phase of chaos control of the predator-prey model with Holling type-III

Cited by 5 publications

References 28 publications

Dynamic Behavior and Bifurcation Analysis of a Modified Reduced Lorenz Model

Dynamic Behavior and Bifurcation Analysis of a Modified Reduced Lorenz Model

Bifurcation Analysis and Chaos Control for Prey-Predator Model With Allee Effect

Exploring chaos and bifurcation in a discrete prey–predator based on coupled logistic map

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