Unstable dimension variability structure in the parameter space of coupled Hénon maps

Coupled maps have been investigated to model the applications of periodic and chaotic dynamics of spatially extended systems. We have studied the parameter space of coupled Hénon maps and showed that attractors possessing unstable dimension variability (UDV) appear for parameters neighbouring the so called shrimp domains, representing parameters leading to stable periodic behaviour. Therefore, the UDV should be very likely to be found in the same large class of natural and man-made systems that present shrimp domains.