Based on recent work [C. J. Tessone, C. R. Mirasso, R. Toral, and J. D. Gunton, Phys. Rev. Lett. 97, 194101 (2006)], the study of coupled bistable oscillators with different sources of diversity is extended. Effects of the correlation between the diversity on the resonant response of the system are discussed. It is found that the diversity of the coupled system, in the form of quenched noise, can induce a resonant effect in response to external signals. The resonance is reduced and even disappears as the correlation length between the diversity increases, while the spatial synchronization is enhanced due to the correlation between the diversity.
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