Numerical simulation in nonlinear dynamic systems with retiming of motions of individual components

摘要

We study differential equations describing nonlinear processes in dynamical systems (macro-systems) that consist of a large number of components (micro-systems) and allow a synchronization in behavior of these components. In physics, these processes underlie the echo phenomena. An empirical solution of such equations is proposed. A solution is given in the form of power series of power series of the spectra of external of external perturbations acting on a macro-system. Numerical simulations of this solution give a good agreement with a number of experimentally observed echo phenomena.