Dynamical Behavior of a Delayed Holling Type‐II Predator‐Prey Model with Predator Cannibalism

Lavanya, R.; Vinoth, S.; Sathiyanathan, K.; Njitacke, Zeric Tabekoueng; Hammachukiattikul, Porpattama; Vadivel, R.

doi:10.1155/2022/4071375

Cited by 4 publications

(3 citation statements)

References 25 publications

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“…Regarding the delay as bifurcating parameter, they discussed the local asymptotic stability and Hopf bifurcation of the positive equilibrium by analyzing the corresponding characteristic equations of linearized systems. Lavanya et al [30] proposed the Holling type-II predator-prey model involving cannibalism and gestation delay in predators and gave the condition for the local stability and Hopf bifurcation analysis for the non-delayed model. Taffo and Siewe [31] examined dynamical behavior of a nonlinear oscillator with symmetric potential that models a quarter-car forced by the road profile under parametric excitation.…”

Section: Introductionmentioning

confidence: 99%

“…Lavanya et al. [30] proposed the Holling type‐II predator‐prey model involving cannibalism and gestation delay in predators and gave the condition for the local stability and Hopf bifurcation analysis for the non‐delayed model. Taffo and Siewe [31] examined dynamical behavior of a nonlinear oscillator with symmetric potential that models a quarter‐car forced by the road profile under parametric excitation.…”

Section: Introductionmentioning

confidence: 99%

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Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback

Hu,

Zhou

2023

Z Angew Math Mech

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In this manuscript, a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback is studied both analytically and numerically. The Hamilton systems of triple‐well and narrow single‐well are discussed in detail. The scenarios of phase portraits and equilibria are given. Homoclinic and heteroclinic orbits are strictly derived. With the Melnikov method, the critical value of chaos arising from homoclinic or heteroclinic intersections is derived analytically. We have discovered some interesting dynamic phenomena, such as uncontrollable time delays with which chaos always occurs for this system. The influence of time‐delay on the chaotic property is also studied rigorously. On the basis of theoretical analysis, some numerical simulations including time histories, phase portraits, bifurcation diagrams, Poincaré sections, Lyapunov exponential spectrums and attractor basins are given. Numerical simulations are consistent with theoretical results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback

Hu,

Zhou

2023

Z Angew Math Mech

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“…Predator-prey interactions have been included in the Lotka-Volterra model for a very long time, see references [1][2][3]. In a similar vein, after the seminal work of Kermack and McKendrick [4], the interaction of the susceptible, infected, and recovered prey has been an interesting topic of study. The original predator-prey model was developed in large part by Vito Volterra and Alfred James Lotka.…”

Section: Introductionmentioning

confidence: 99%

The Effect of Fear on a Diseased Prey–Predator Model with Predator Harvesting

Natesan,

Shanmugam,

Manickasundaram

et al. 2023

Asec 2023

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Chaos Control, Codimension‐One and Codimension‐Two 1 : 2 Strong Resonance Bifurcation Analysis of a Predator‐Prey Model with Holling Types I and III Functional Responses

Khan,

Naqvi,

Ahmed

et al. 2024

Complexity

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We study the existence of fixed points, local stability analysis, bifurcation sets at fixed points, codimension‐one and codimension‐two bifurcation analysis, and chaos control in a predator‐prey model with Holling types I and III functional responses. It is proven that the model has a trivial equilibrium point for all involved parameters but interior and semitrivial equilibrium solutions under certain model parameter conditions. Furthermore, local stability at trivial, semitrivial, and interior equilibria using the theory of linear stability is investigated. We have also explored the bifurcation sets for trivial, semitrivial, and interior equilibria and proved that flip bifurcation occurs at semitrivial equilibrium. Furthermore, it is also proven that Neimark–Sacker bifurcation as well as flip bifurcation occurs at an interior equilibrium solution, and in addition, at the same equilibrium solution, we also studied codimension‐two 1 : 2 strong resonance bifurcation. Then, OGY and hybrid control strategies are employed to manage chaos in the model under study, which arises from Neimark–Sacker and flip bifurcations, respectively. We have also examined the preservation of the positive solution of the understudied model. Finally, numerical simulations are given to verify the theoretical results.

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Dynamical Behavior of a Delayed Holling Type‐II Predator‐Prey Model with Predator Cannibalism

Cited by 4 publications

References 25 publications

Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback

Orbits and chaos of a two‐fluid magnetized plasma oscillator subjected to parametric excitation with square delayed feedback

The Effect of Fear on a Diseased Prey–Predator Model with Predator Harvesting

Chaos Control, Codimension‐One and Codimension‐Two 1 : 2 Strong Resonance Bifurcation Analysis of a Predator‐Prey Model with Holling Types I and III Functional Responses

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