An approximation to the Benjamin-Bona-Mahony equation

Baron-Pertuz, Cristian-Fabian; Marin-Ramirez, Ana-Magnolia; Ortiz-Ortiz, Ruben-Dario

doi:10.12988/ijma.2014.410335

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2018

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“…In [10] was based on finding solutions for the combined sinh-cosh-Gordon equation using Hamiltonnian systems at a specific region on the plane in which these do not have periodic orbits. In [11] it was constructed a solution of the nonlinear Benjamin-Bona-Mahony equation using Fourier transform and Neumann series. In [12] it was obtained the general result of a Duffing differential equation, which it has periodic orbits, but when it was applied the Poincare transformation; the new system obtained gives a dynamical system on the plane without periodic orbits.…”

Section: Introductionmentioning

confidence: 99%

Stability in a Holling-Tanner predator-prey model like a Kolmogorov system without periodic orbits via Dulac functions

Marín¹,

Ortiz-Ortiz²,

Gutiérrez³

2018

ces

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In this work, we find Dulac functions for Kolmogorov systems which can be applied to biological models in population. With a well choose of the Dulac function h we obtain stability and a phase diagram without periodic orbits. We prove that there are not periodic orbits at the interior of the first quadrant on the plane. We also obtain a generalized Kolmogorov system and apply this to the Holling-Tanner model and we use time series to understand its behaviour.

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Section: Introductionmentioning

confidence: 99%