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We investigate the spatio-temporal dynamics of coupled chaotic systems withnonlocal interactions, where each element is coupled to its nearest neighborswithin a finite range. Depending upon the coupling strength and couplingradius, we find characteristic spatial patterns such as wave-like profiles andstudy the transition from coherence to incoherence leading to spatial chaos. Weanalyze the origin of this transition based on numerical simulations andsupport the results by theoretical derivations identifying a critical couplingstrength and a scaling relation of the coherent profiles. To demonstrate theuniversality of our findings we consider time-discrete as well astime-continuous chaotic models realized as logistic map and R\"ossler or Lorenzsystem, respectively. Thereby we establish the coherence-incoherence transitionin networks of coupled identical oscillators.

Transition from spatial coherence to incoherence in coupled chaotic systems