A generic, hard transition to chaos

[摘要] A hard-in-amplitude transition to chaos in a class of dissipative flows of broad applicability is presented. For positive values of a parameter Gamma, no matter how small, a fully developed chaotic attractor exists within some domain of additional parameters, whereas no chaotic behavior exists for Gamma less than or equal to 0. As Gamma is made positive, an unstable fixed point reaches an invariant plane to enter a phase half-space of physical solutions; the ghosts of a line of fixed points and a rich heteroclinic structure existing at Gamma = 0 make the limits t --> +infinity, Gamma --> +0 non-commuting, and allow an exact description of the chaotic flow. The formal structure of flows that exhibit the transition is determined. A subclass of such flows (coupled oscillators in near-resonance at any 2 : q frequency ratio, with Gamma representing linear excitation of the first oscillator) is fully analysed.

[发布日期] 1995-12-15

[关键词] chaos;maps;oscillators;resonances