Limit cycles and singular point quantities for a 3D Lotka-Volterra system. (English) Zbl 1220.34051

Wang, Qinlong; Huang, Wentao; Li, Bai-Lian

Appl. Math. Comput. 217, No. 21, 8856-8859 (2011).

Summary: Four limit cycles are constructed for a three dimensional Lotka-Volterra system. This gives a good example to the cyclicity of 3D Lotka-Volterra systems. A recursion formula for the computation of the singular point quantities is given for the corresponding Hopf bifurcation equation. The expressions of focal values are simpler, and the formula is readily done using computer symbol operation system such as Mathematica due to its linearity.

MSC:

34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C07	Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
34C45	Invariant manifolds for ordinary differential equations
34C23	Bifurcation theory for ordinary differential equations
92D25	Population dynamics (general)

Keywords:

3D Lotka-Volterra system; Hopf bifurcation; singular point quantities; center manifold

Software:

Mathematica

References:

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