Simulation and numerical analysis of dynamical systems with competitive interactions

Authors

DOI:

https://doi.org/10.15587/2312-8372.2015.41156

Keywords:

Lotka-Volterra model, model perturbations, stability problems, periodic solutions, attractor, limit cycle

Abstract

The effects of the destabilization of competitive coexistence "populations" – actors described by a system of differential equations of Lotka-Volterra for three classes of objects: the economic system "producer-mediator", the Keynesian model of the economy of several countries, and weak sinusoidal external influences on the rate of "reproduction". The stability of such systems is investigated. Numerical solutions are found at frequencies of exposure close to the frequency of the unperturbed system.

Such systems are soft classical models of many real objects in environment, economy and other areas, and their studies are relevant.

It is known that the corresponding system of nonlinear equations, especially with the right part of the disturbed, generally cannot be solved. Numerical experiment revealed bifurcation when changing the amplitudes of n, and the period of the disturbance . Trophic parameters of the unperturbed system do not lead to bifurcations for the classical Lotka-Volterra system.

The studies found that the variation of the amplitude (in the range 0-0,15) lead to the transition of the system of periodic motions to sustainable growth, and then to chaotic oscillations. So, bifurcation introduces asymmetry in the structure of the characteristic exponents, and with it the instability and "withdrawal" of path to infinity. There are possible both monotonous and chaotic type.

Author Biography

Валид Ахмед Альрефаи, Kharkiv National University of Radio Electronics, 14, Lenin av., Kharkiv, Ukraine, 61166

Post-graduate student

Department of Applied Mathematics

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Published

2015-04-02

How to Cite

Альрефаи, В. А. (2015). Simulation and numerical analysis of dynamical systems with competitive interactions. Technology Audit and Production Reserves, 2(5(22), 36–41. https://doi.org/10.15587/2312-8372.2015.41156

Issue

Vol. 2 No. 5(22) (2015): Mathematical modeling. Information and control systems

Section

Mathematical Modeling: Original Research

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Copyright (c) 2016 Валид Ахмед Альрефаи

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