The Integrability and the Zero-Hopf Bifurcation of the Three Dimensional Lotka-Volterra Systems.

Autor:	Salih, Rizgar H.
Předmět:	MATHEMATICAL models of Hopf bifurcations BIFURCATION theory LOTKA-Volterra equations EIGENVALUES COMBINATORIAL dynamics CRITICAL point (Thermodynamics) NONLINEAR oscillations
Zdroj:	AIP Conference Proceedings; 2018, Vol. 1926 Issue 1, p1-8, 8p
Abstrakt:	This paper is devoted to study the zero-Hopf bifurcation of the three dimensional Lotka-Volterra systems. The explicit conditions for the existence of two first integrals for the system and a line of singularities with zero eigenvalue are given. We characteristic the parameters for which a zero-Hopf equilibrium point takes place at any points on the line. We prove that there are three 3-parameter families exhibiting such equilibria. The averaging theory of the first order is also applied but any information about the possible periodic orbits bifurcating from the zero-Hopf equilibria is not provided by this theorem. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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