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Seven large-amplitude limit cycles in a cubic polynomial system. (English) Zbl 1111.37035
Summary: The problem of limit cycles bifurcated from the equator for a cubic polynomial system is investigated. The best result so far in the literature for this problem is six limit cycles. By using the method of singular point value, we prove that a cubic polynomial system can bifurcate seven limit cycles from the equator. We also find that a rational system has an isochronous center at the equator.
MSC:
37G15Bifurcations of limit cycles and periodic orbits
34C07Theory of limit cycles of polynomial and analytic vector fields
34C05Location of integral curves, singular points, limit cycles (ODE)
37C10Vector fields, flows, ordinary differential equations