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Control of limit cycle bifurcations in the Kukles cubic system

Valery Gaiko, Jean-Marc Ginoux, Cornelis Vuik
We carry out the global bifurcation analysis of the Kukles system representing a planar polynomial dynamical system with arbitrary linear and cubic right-hand sides and having an anti-saddle at the origin. Using our geometric approach, we control all possible limit cycle bifurcations and solve the problem on the maximum number and distribution of limit cycles in this system. Numerical experiments are done to illustrate the obtained results.
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