CUBIC AND QUARTIC PLANAR DIFFERENTIAL SYSTEMS WITH EXACT ALGEBRAIC LIMIT CYCLES

Ahmed Bendjeddou, Rachid Cheurfa
2011 Electronic Journal of Differential Equations   unpublished
We construct cubic and quartic polynomial planar differential systems with exact limit cycles that are ovals of algebraic real curves of degree four. The result obtained for the cubic case generalizes a proposition of [9]. For the quartic case, we deduce for the first time a class of systems with four algebraic limit cycles and another for which nested configurations of limit cycles occur.
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