Response of Complex Systems to Complex Perturbations: Complexity Matching

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We argue that complex systems, defined as non-Poisson renewal process, with complexity index μ, exchange information through complexity matching. We illustrate this property with detailed theoretical and numerical calculations describing a system with complexity index μₛ perturbed by a signal with complexity index μₚ. We focus our attention on the case 1.5 ≤ μₛ ≤ 2 and 1 ≤ μₚ ≤ 2. We show that for μₛ ≥ μₚ, the system S reproduces the perturbation, and the response intensity increases with increasing μₚ. The maximum intensity is realized by the matching condition μₚ = μₛ. For μₚ > μₛ the response intensity dies out as 1/tμᵖ⁻μˢ.