Response of Complex Systems to Complex Perturbations: the Complexity Matching Effect (original) (raw)

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/t µ P −µ S .