Nonstationary Process: Nonstationary Bifurcation Maps, Evolutionary Dynamics
The study presented in this paper is one of a series of papers published by the authors on nonstationary problems. It addresses itself to the characterization of the types of dynamical responses and their ranges contained in the time flow of the Duffing nonlinear, nonstationary, dissipative, forced oscillator. A new effective method - a Nonstationary Bifurcation Map (EI-Lu map) - has been introduced by the authors that allows us to do precisely this. This new technique is by far more advantageous than the customary methods in use: the phase portrait or Poincare maps. The latter may give inadequate information because of the overlapping dynamical responses contained within ranges of time. The main feature of nonstationary processes is that the nonstationary responses are transient. The phenomena of the transiency are presented in detail. Significant cases are those when the non-stationary transmission of the signals crosses different nonstationary bifurcation boundaries. This is significant because most of dynamical-biological activities occur in the regions between order and chaos. It characterizes nonstationary dynamical processes. The possibility of constructing responses for arbitrary small nonstationary inputs may be used as nonstationary perturbations, replacing customary perturbations of integrable Hamiltonians.
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Evan-Iwanowski, R. M. and Lu, C. H., "Nonstationary Process: Nonstationary Bifurcation Maps, Evolutionary Dynamics" (2000). Scopus Export 2000s. 1222.