  We present theoretical and experimental studies on pattern formation with
bistable dynamical units coupled in a star network configuration. By applying a
localized perturbation to the central or the peripheral elements, we
demonstrate the subsequent spreading, pinning, or retraction of the
activations; such analysis enables the characterization of the formation of
stationary patterns of localized activity. The results are interpreted with a
theoretical analysis of a simplified bistable reaction-diffusion model. Weak
coupling results in trivial pinned states where the activation cannot
propagate. At strong coupling, uniform state is expected with active or
inactive elements at small or large degree networks respectively. Nontrivial
stationary spatial pattern, corresponding to an activation pinning, is
predicted to occur at intermediate number of peripheral elements and at
intermediate coupling strengths, where the central activation of the network is
pinned, but the peripheral activation propagates toward the center. The results
are confirmed in experiments with star networks of bistable electrochemical
reactions. The experiments confirm the existence of the stationary spatial
patterns and the dependence of coupling strength on the number of peripheral
elements for transitions between pinned and retreating or spreading fronts in
forced network configurations (where the central or periphery elements are
forced to maintain their states).
