Quadratic systems without periodic orbits

Marin-Ramirez, Ana-Magnolia; Rodriguez-Ceballos, Joel-Arturo; Ortiz-Ortiz, Ruben-Dario

doi:10.12988/ijma.2014.48254

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Cited by 3 publications

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“…where Proof. Now we consider the differential equation for the Dulac function h (see [6], [7], [8], [10])…”

Section: Dynamical Systemmentioning

confidence: 99%

An approximation to the Benjamin-Bona-Mahony equation

Baron-Pertuz¹,

Marin-Ramirez²,

Ortiz-Ortiz³

2014

ijma

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“…where Proof. Now we consider the differential equation for the Dulac function h (see [6], [7], [8], [10])…”

Section: Dynamical Systemmentioning

confidence: 99%

An approximation to the Benjamin-Bona-Mahony equation

Baron-Pertuz¹,

Marin-Ramirez²,

Ortiz-Ortiz³

2014

ijma

Self Cite

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“…A Dulac function for the Kolmogorov system was found [4]. In [6] it were studied quadratic systems using certain Dulac functions and a geometric method. In [7] it was found a general 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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“…A Dulac function for a quadratic system was found in (Marin et al, 2013b). A Dulac function and a geometric method for a quadratic system was studied in (Marin-Ramirez et al, 2014). In this article our objective is construct dynamical systems that does not have periodic orbits using Dulac functions and we use the following criterion to show the non-existence of periodic orbits.…”

Section: Introductionmentioning

confidence: 99%