Study of chaos in double coupled oscillators system based on topological horseshoe theory
Fangyan Yang · Journal of Computer Applications · 2013
Recently,collective chaos in coupled oscillators networks has become a new hot spot in the chaos study.On account of short growing history of collective chaos and lacking of mature theories and methods,the main means of research is still concentrated on the rough ones such as numerical computation,power spectrum and Lyapunov exponent,which are not strict judgment in mathematics and hard to describe the mechanism of chaos.By means of topological horseshoe theory,the authors studied deeply collective chaos of one four-dimensional continuous system consisting of a pair of coupled oscillators and found that topological horseshoe with expanding in one direction in the phase space of the corresponding Poincare map.It not only strictly demonstrates by numerical way that the coupled oscillator system is chaotic,but also reveals the dynamic mechanism of chaos.