Stabilization of unstable limit cycles of two-dimensional dynamical systems (Q1128385)

Let \(\Gamma\) be a closed orbit with period \(T\) of the two-dimensional system \(dz/dt= F(z)\). Let \(G:\mathbb R^2\times \mathbb R\to \mathbb R^2\), \(H,Q: \mathbb R^2\times \mathbb R\to \mathbb R\) be mappings such that \(G(p,T)= 0\), \(H(p,T)= Q(p,T)= 0\) for every \(p\in\Gamma\). The author introduces the mapping \(M: z_{n+ 1}= G(z_n, t_n)+ u_n\widetilde\delta\), \(u_{n+ 1}= H(z_n, t_n)+ \beta u_n\), \(t_{n+ 1}= Q(z_n, t_n)+ t_n\) with \(\widetilde\delta= (0,\delta)^T\) having \((p,0,T)\) as fixed point for all \(p\in\Gamma\). The author derives sufficient conditions for the stabilizability of a fixed point of \(M\).