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Interplay Between Structural Randomness, Composite Disorder, and Electrical Response: Resonances and Transient Delays in Complex Impedance Networks

We study the interplay between structural and conductivity (composite) disorder and the collective electrical response in random networks models. Translating the problem of time-dependent electrical response (resonance and transient relaxation) in binary random composite networks to the framework of generalized eigenvalues, we study and analyze the scaling behavior of the density of resonances in these structures. We found that by controlling the density of shortcuts (topological randomness) and/or the composite ratio of the binary links (conductivity disorder), one can effectively shape resonance landscapes, or suppress long transient delays in the corresponding random impedance networks.