Nonlinear differential equations and dynamical systems
Nonlinear differential equations and dynamical systems
Averaging analysis of a perturbated quadratic center
Nonlinear Analysis: Theory, Methods & Applications
Limit Cycles for Multidimensional Vector Fields. The Elliptic Case
Journal of Dynamical and Control Systems
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Perturbing the system $\dot{x} = - y{\left( {1 + x} \right)},\,\dot{y} = x{\left( {1 + x} \right)},\,\dot{z} = 0$ inside the family of polynomial differential systems of degree n in $\mathbb{R}^{3}$ , we obtain at most n 2 limit cycles using the first-order averaging theory. Moreover, there exist such perturbed systems having at least n 2 limit cycles.