Multiple limit cycles bifurcation from the degenerate singularity for a class of three-dimensional systems.(English)Zbl 1387.34061
The authors consider three-dimensional autonomous systems \[{dx\over dt}= Ax+ \text{h.o.t.},\] where the matrix \(A\) is nilpotent and has two zero eigenvalues and one negative eigenvalue. They describe procedures to determine the multiplicity of the equilibrium at the origin which provides an upper bound for the number of limit cycles bifurcating from the origin. An example is presented.
Reviewer: Klaus R. Schneider (Berlin)
MSC:
| 34C23 | Bifurcation theory for ordinary differential equations |
| 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 |
Keywords:
quasi-Lyapunov constant;degenerate singularity;limit cycles bifurcation;three-dimensional systemCite
Full Text:DOI
References:
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