Chaotic behavior analysis based on corner bifurcations (Q1036639)

The authors consider a piecewise smooth system \[ \dot x = F_1(x)\text{ if }H_1(x) \geq 0\text{ or }H_2(x) \geq 0, \] \[ \dot x = F_2(x)\text{ if }H_1(x) < 0\text{ and }H_2(x) < 0, \] where \(H_1\) and \(H_2\) are \(C^1\) functions on an open set in \(\mathbb R^n\), \(n \geq 3\), whose codimension-one zero sets intersect transversally along a smooth codimension-two surface. This is a ``corner'' set. The authors show how in this setting there can occur a robust path to chaos: chaotic dynamics that exist in a neighborhood of a particular value of a bifurcation parameter.