Abstract :

We investigate an inhomogeneous lattice of coupled logistic maps numerically with respect to inhomogenity constant $\gamma$ and the coupling constant $\epsilon$. In our model inhomogeity appears in the form of different values of the map parameter in different sites. The phase diagram of the model in $\gamma-\epsilon$ plane gives five qualitatively different solutions. They are synchronized solution, non-synchronized solution fixed in time, periodic in time, quasi-periodic in time and spatio- temporal chaotic solution. Our system exhibits tangent bifurcation from synchronized solution to non-synchronized steady solution, period doubling bifurcation from non-synchronized steady solution to periodic solution and Neimark Sacker (Hopf) bifurcation from non-synchronized steady solution to quasiperiodic solution. We illustrate our results using time plot, spacetime plot, Fourier transform, bifurcation diagram, stability matrix.