Analyzing the Synchronization of Rössler Systems – When Trigger-And-Reinject Is Equally Important as the Spiral Motion
An-Liang Cheng1*, Yih-Yuh Chen1
1Department of Physics, National Taiwan University, Taipei, Taiwan
* Presenter:An-Liang Cheng, email:phairst@gmail.com
The study of the synchronous stability of two coupled Rössler attractors sometimes can be effectively described by approximating the trajectory on the attractor as a planar outward spiral. We show that this is true only when one is dealing with the spiral-type attractor. But when the funnel-type attractor which exhibits the motion of the trigger-and-reinject is equally important as the spiral motion is
encountered, a properly constructed time-weighted average must be used to yield a prediction that agrees well with the numerical results. We also analytically show the time evolution of the separation vector, and demonstrate why this study matters when one tries to perform the time-weighted average.


Keywords: Synchronization of chaos, Rössler attractor, Funnel-type Rössler attractor, Simple core