Stability analysis of fixed point of fractional-order coupled map lattices

We study the stability of synchronized fixed-point state for linear fractional-order coupled map lattice(CML). observe that eigenvalues connectivity matrix determine as integer-order CML. These can be determined exactly in certain cases. find exact bounds one-dimensional lattice with translationally invariant coupling using theory circulant matrices. This extended to any finite dimension. Similar analysis carried out fixed point nonlinear fractional maps where Jacobian play same role. The is generic and demonstrates a pivotal role even maps.