Nonstationary process: Nonstationary bifurcation maps, evolutionary dynamics (Q1566999)

A new numerical method, a nonstationary bifurcation map for dynamics responses, is given to identify individual types of dynamical responses (single, multiple resonance, periodic or chaotic responses), and to describe these responses in terms of time cycles of forcing frequency. This new technique is by far more advantageous than the usual methods in use: the phase portrait or Poincaré maps. The main feature of nonstationary processes is that the nonstationary responses are transient. In the most important cases, the nonstationary transmission of signals crosses different nonstationary bifurcation boundaries. The authors show that the possibility of constructing responses for arbitrary small nonstationary inputs may be used as nonstationary perturbations, replacing traditional perturbations of integrable Hamiltonians.