We explore the dynamics of a piecewise linear normal form map under the condition that the map is contractive in one compartment and expansive in the other. In particular, we analyze the transition from a mode-locked periodic orbit to a chaotic orbit. It occurs through the following sequence: first homoclinic contact followed by homoclinic intersection, which is again followed by a second homoclinic contact. We have shown that after the second homoclinic contact, a circular-shaped strange attractor with an infinite number of non-smooth folds is created. The mechanism of this chaotic behavior is explained in terms of tangencies with the stable foliation of the saddle fixed point.
Dr. Biswambhar Rakshit, Banerjee, S., and Aihara, K., “Circle Like Strange Attractor in a Piecewise Smooth Map”, IFAC Proceedings Volumes, vol. 45, pp. 81 - 86, 2012.