Imperfect bifurcation of systems with slowly varying parameters and application to Duffing's equation (Q1841452)

The authors consider bifurcation problems of the form \(\dot{x}=f(x,\lambda,\alpha)\), \(x\in \mathbb{R}^n\), \(\lambda=\lambda(\varepsilon t)\in \mathbb{R}\), \(\alpha \in \mathbb{R}\), where the parameter \(\lambda\) varies slowly \((0\leq \varepsilon \leq 1)\) with time, and \(0\leq \alpha \leq 1\) is an imperfect bifurcation parameter. The authors suggest a new qualitative method for theoretical analysis of these bifurcation problems, and apply their results to time-dependent bifurcations of Duffing's equation.