Fractal Dimension as a Criterion for Systems Stability

摘要

It is shown that a complex system can be described in terms of fractal geometry, provided that its behavior is governed by the Kolmogorov-Fokker-Planck equations with the right-hand sides linear with respect to the unknown function. In this case, a fractal dimension is a metacharacteristic of the instability of the system. Inequalities for a fractal dimension are obtained that can be used as the instability criteria indicating that the state of the system can belong to the domains of flicker noise or weak chaos.