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 solutions such as temporally frozen kinks, spatiotemporally synchronized solutions and kink induced temporally intermittent solutions appear in different regions of parameter space for this system and bifurcations are seen from one type of solution to another. The upper boundaries of the regions where the 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 boundaries. Our characterisers could be of utility in other situations as well.
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