A geometric method for detecting chaotic dynamics

[摘要] A new method of detection of chaos in dynamical systems generated by time-periodic nonautonomous differential equations is presented. It is based on the existence of some sets (called periodic isolating segments) in the extended phase space, satisfying some topological conditions. By chaos we mean the existence of a compact invariant set such that the Poincare map is semiconjugated to the shift on two symbols and the counterimage (by the semiconjugacy) of any periodic point in the shift contains a periodic point of the Poincare map. As an application we prove that the planar equation z = (1 + e(t phi t) \z\(2))(z) over bar generates chaotic dynamics provided 0 < phi less than or equal to 1/288. (C) 1997 Academic Press.

[发布日期] 1997-03-20