Polynomial Differential System with Ten Limit Cycles at Infinity
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Abstract:
An indirect method is used to study bifurcations of limit cycles at infinity for a class of seventh-order polynomial differential system.First,the problem for bifurcations of limit cycles in the system at infinity is transformed into that at the origin.By the computation of fist 98 singular quantities,the conditions of the origin(correspondingly,infinity) to be the highest degree fine focus are derived.Finally,the system that bifurcates nine limit cycles in the neighborhood of infinity is constructed,which is proved that ten limit cycles can bifurcated at infinity for a class of seven-order polynomial system firstly.
