Numerical research of stability in Lotka-Volterra systems with perturbed right side

Authors

  • Мохаммад Ракан Абед Алнаби Альджаафрех Kharkiv National University of Radio Electronics, Lenina 14, Kharkov, Ukraine, 61166, Ukraine https://orcid.org/0000-0002-8326-2764

DOI:

https://doi.org/10.15587/2312-8372.2014.25275

Keywords:

Lotka-Volterra model, stability problems, phase space

Abstract

The basic effects and patterns that characterize the model of coexistence of two species with weak sinusoidal external effect on the reproduction rate are considered. Solving Lotka-Volterra differential equations describes the ecosystem behavior. Numerical solutions for exposure frequencies, close to the frequency of an unperturbed system cycle are found. The stability of such a non-autonomous system is studied. It is determined that the periodic effect on the population, for example, by changing nutrition or hunting leads to a non-periodic system dynamics. Various forms of irregular behavior of “predators” and “victims” appear in the phase patterns for similar perturbations. All this confirms that even relatively simple models of ecosystems reveal their instability, i.e., sensitivity to small external perturbations.

The parameters of perturbations, leading in the proximity of resonant perturbation to both non-periodic growth of populations and non-periodic motions over a finite area, or to stabilization around zero, are defined. Herewith, extinction of populations is quite possible. The obtained results can be used by experts in the field of ecology and economy.

Author Biography

Мохаммад Ракан Абед Алнаби Альджаафрех, Kharkiv National University of Radio Electronics, Lenina 14, Kharkov, Ukraine, 61166

Graduate student

Department of Applied Mathematics

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Published

2014-05-29

How to Cite

Альджаафрех, М. Р. А. А. (2014). Numerical research of stability in Lotka-Volterra systems with perturbed right side. Technology Audit and Production Reserves, 3(1(17), 20–22. https://doi.org/10.15587/2312-8372.2014.25275

Issue

Vol. 3 No. 1(17) (2014): Technology audit

Section

Technology audit

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