On the stabilization of stationary points of chaotic dynamical systems (Q1595542)

Consider the autonomous system \[ dx/dt= F(x,p)\tag{\(*\)} \] with \(p\in \mathbb R\). Let \(x^*(p)\) be an equilibrium point to \((*)\) which is stable for \(p\leq p_*\), and unstable for \(p> p_*\). The author introduces the system \[ dx/dt= F(x,p)+ \varepsilon(q-p),\quad dq/dt= Q(x,p)+ \beta(q- p)\tag{\(**\)} \] with \(Q(x_*(p),p)= 0\), \(\varepsilon= (\varepsilon_1,\dots, \varepsilon_m)\) and \(\beta\in\mathbb R\) are parameters. The author derives conditions such that \((x^*(p),p)\) is a stable equilibrium point to \((**)\) for \(p_*\leq p\leq p_*+ \nu\) where \(\nu\) is some positive number.