  The synchronization behavior of delay coupled chaotic smooth unimodal maps
over a ring network with stochastic switching of links at every time step is
reported in this paper. It is observed that spatiotemporal synchronization
never appears for nearest neighbor connections; however, stochastic switching
of connections with homogeneous delay $(\tau)$ is capable of synchronizing the
network to homogeneous steady state or periodic orbit or synchronized
chaotically oscillating state depending on the delay parameter, stochasticity
parameter and map parameters. Linear stability analysis of the synchronized
state is done analytically for unit delay and the value of the critical
coupling strength, at which the onset of synchronization occurs is determined
analytically. The logistic map $rx(1-x)$ (a smooth unimodal map) is chosen for
numerical simulation purpose. Synchronized steady state or synchronized
period-2 orbit is stabilized for delay $\tau=1$. On the other hand for delay
$\tau=2$ the network is stabilized to the fixed point of the local map.
Numerical simulation results are in good agreement with the analytically
obtained linear stability analysis results. Another interesting observation is
the existence of synchronized chaos in the network for delay $\tau>2$.
Calculating synchronization error and plotting time series data and Poincare
first return map the existence of synchronized chaos is confirmed. The results
hold good for other smooth unimodal maps also.
