TITLE:
Describing Chaos of Continuous Time System Using Bounded Space Curve
AUTHORS:
Binghua Huang, Yafen Wei, Ying Huang, Yongqing Liang
KEYWORDS:
Nonlinear Oscillation, Lorenz Equation, Chaos, Chua’s Circuit, Lossless Circuit, Space Curve
JOURNAL NAME:
Journal of Modern Physics,
Vol.5 No.15,
September
26,
2014
ABSTRACT: The
qualitative solutions of dynamical system expressed with nonlinear differential
equation can be divided into two categories. One is that the motion of phase
point may approach infinite or stable equilibrium point eventually. Neither
periodic excited source nor self-excited oscillation exists in such nonlinear
dynamic circuits, so its solution cannot be treated as the synthesis of multiharmonic.
And the other is that the endless vibration of phase point is limited within
certain range, moreover possesses character of sustained oscillation, namely
the bounded nonlinear oscillation. It can persistently and repeatedly vibration
after dynamic variable entering into steady state; moreover the motion of phase
point will not approach infinite at last; system has not stable equilibrium
point. The motional trajectory can be described by a bounded space curve. So
far, the curve cannot be represented by concretely explicit parametric form in
math. It cannot be expressed analytically by human. The chaos is a most universally
common form of bounded nonlinear oscillation. A number of chaotic systems, such
as Lorenz equation, Chua’s circuit and lossless system in modern times are some
examples among thousands of chaotic equations. In this work, basic properties
related to the bounded space curve will be comprehensively summarized by
analyzing these examples.