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

Abstract

In this paper we suggest a new characteristic of chaos which is the evolutionary order parameter. This parameter allows to determine bifurcation regimes by use of realization of a dynamical system. Unlike existing methods for constructing bifurcation diagrams, this method determines a state of the dynamical system more precisely. As a signal generator we select dynamical systems, such as logistic map, Henon map, the new bursting map, modified Lorenz system. We present bifurcation diagrams depending on evolutionary order parameter.