A dynamic system has a finite number of limit cycles. However,udfinding the upper bound of the number of limit cycles is an openudproblem for general non-linear dynamical systems. In thisudpaper, we investigated a class of non-linear systems underudperturbations. We proved that the upper bound of the number of zeros ofud the related elliptic integrals of the given system is 7n + 5 including multiple zeros, which also gives the upper bound of the number of limit cycles for the given system.
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