Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation

Kadeřábek, Zdeněk

doi:10.5817/am2016-1-49

Arch. Math. (Brno)

2016

DOI: 10.5817/am2016-1-49

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Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation

Zdeněk Kadeřábek¹

Abstract: The modified generalized Van der Pol-Mathieu equation is generalization of the equation that is investigated by authors Momeni et al. (2007), Veerman and Verhulst (2009) and Kadeřábek (2012). In this article the Bautin bifurcation of the autonomous system associated with the modified generalized Van der Pol-Mathieu equation has been proved. The existence of limit cycles is studied and the Lyapunov quantities of the autonomous system associated with the modified Van der Pol-Mathieu equation are computed.

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Bifurcation Analysis of a Modified Leslie–gower Predator–prey Model With Hunting Cooperation and Favorable Additional Food for Predator

Samaddar¹,

Dhar²,

Bhattacharya³

et al. 2023

J. Biol. Syst.

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In this paper, we consider a modified Lasslie–Gower-type predator–prey model with the effect of hunting cooperation and favorable additional food for predator. We establish the conditions of positivity, boundedness, and permanence of solutions of the proposed model. Along with the trivial, predator free, prey free equilibrium points the system contains at most two coexistence equilibrium points. The system experiences the transcritical, saddle-node, Hopf, cusp, Bautin, and Bogdanov–Takens bifurcation depending on the model parameters. All the theoretical analyses are verified using numerical simulations. It is numerically established that the cooperation and extra food have high impact on the model dynamics.

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Bifurcation Analysis of a Modified Leslie–gower Predator–prey Model With Hunting Cooperation and Favorable Additional Food for Predator

Samaddar¹,

Dhar²,

Bhattacharya³

et al. 2023

J. Biol. Syst.

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Periodic solutions of Liénard–Mathieu differential equation with a small parameter

Kalas

2017

Georgian Mathematical Journal

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Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation

Cited by 2 publications

References 7 publications

Bifurcation Analysis of a Modified Leslie–gower Predator–prey Model With Hunting Cooperation and Favorable Additional Food for Predator

Bifurcation Analysis of a Modified Leslie–gower Predator–prey Model With Hunting Cooperation and Favorable Additional Food for Predator

Periodic solutions of Liénard–Mathieu differential equation with a small parameter

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