Limit Cycle Bifurcations from a Nilpotent Focus or Center of Planar Systems
Copyright policy )Limit Cycle Bifurcations from a Nilpotent Focus or Center of Planar Systems
We study analytic properties of the Poincaré return map and generalized focal values of analytic planar systems with a nilpotent focus or center. We use the focal values and the map to study the number of limit cycles of this kind of systems and obtain some new results on the lower and upper bounds of the maximal number of limit cycles bifurcating from the nilpotent focus or center. The main results generalize the classical Hopf bifurcation theory and establish the new bifurcation theory for the nilpotent case.
- Shangrao Normal University China (People's Republic of)
- Shanghai Normal University
- SHANGHAI NORMAL UNIVERSITY China (People's Republic of)
- University of Maribor Slovenia
- Shanghai Normal University
mathematic, Bifurcation theory for ordinary differential equations, limit cycles, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, info:eu-repo/classification/udc/517.9, matematika, bifurkacija, Mathematics - Classical Analysis and ODEs, bifurcation, QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, center problem, Periodic solutions to ordinary differential equations, limitni cikli, problem centra, Mathematics
mathematic, Bifurcation theory for ordinary differential equations, limit cycles, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, info:eu-repo/classification/udc/517.9, matematika, bifurkacija, Mathematics - Classical Analysis and ODEs, bifurcation, QA1-939, Classical Analysis and ODEs (math.CA), FOS: Mathematics, center problem, Periodic solutions to ordinary differential equations, limitni cikli, problem centra, Mathematics
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