New method of investigating of bifurcation regimes by use of realizations from a dynamical system

Abstract

At the present time constructing of bifurcation diagrams for a nonlinear dynamical system can be realized by use of a certain parameter which changes the state of the system. Therefore it is impossible to construct a bifurcation diagram of a dynamical system without of using an order parameter of the dynamical system. A lot of natural phenomena can be described without of using an order parameter of the dynamical system. For example, time realizations of astronomical processes, changes of weather, earthquake magnitude, etc., doesn’t contain an order parameter. Naturally, we arise the question: is it possible to construct a bifurcation diagram without the order parameter of a dynamical system? To solve this problem we propose the new expression for the order parameter of an evolutionary process. This option allows constructing a bifurcation diagram for a realization without knowing the equation describing a dynamical system. The presented examples of bifurcation diagrams are shown universality of the method.