New characterisers of bifurcations from kink solutions in a coupled sine circle map lattice

Kink solutions in coupled sine circle map lattices demonstrate interesting bifurcation behavior. These are illustrated by the study of spatial period two kink solutions for this system. Different types of spatiotemporal solut ions such as temporally frozen kinks, spatiotemporally synchronized solutio ns and kink induced temporally intermittent solutions appear in different r egions of parameter space for this system and bifurcations are seen from on e type of solution to another. The upper boundaries of the regions where th e kinks are stable can be picked up by linear stability analysis. However, the eigenvalues of the stability matrix do not cross the unit circle along the lower stability boundaries, although the nature of the solution changes . Thus linear stability analysis is not sufficient to identify these lower boundaries. Hence we have proposed new characterisers which are capable of identifying such boundaries. Our identifiers successfully pick up the lower boundaries missed by linear stability analysis as well as the upper bounda ries. Our characterisers could be of utility in other situations as well.