Bifurcations near 1:2 subharmonic resonance in a structural dynamics model
The paper deals with the two-parameter family of ordinary differential equations (1) \(\dot u= F(u, \alpha)\), \((u, \alpha)\in \mathbb{R}^d\times \mathbb{R}^2\), \(d\geq 3\), where \(F\) is of class \(C^r\), \(r\geq 4\). The main assumptions are \(u= 0\) is an equilibrium point for all \(\alpha\) in \(\mathbb{R}^2\), and when \(\alpha= 0\) there is a homoclinic solution \(U_0(t)\) of \(u= 0\) and \(u= 0\) undergoes a supercritical Hopf bifurcation. The objective of the paper is to study the generic codimension two bifurcations of such Sil'nikov-Hopf point. Exploiting the center- exponential expansion of Deng, the authors generalize earlier results of Sil'nikov to Hopf points.
scientific article; zbMATH DE number 770018
scientific article