This type of synchronization occurs mainly when the coupled chaotic oscillators are different, although it has also been reported between identical oscillators. Given the dynamical variables (x1,x2,,...,xn) and (y1,y2,,...,ym) that determine the state of the oscillators, generalized synchronization occurs when there is a functional, Φ, such that, after a transitory evolution from appropriate initial conditions, it is =Φ. This means that the dynamical state of one of the oscillators is completely determined by the state of the other. When the oscillators are mutually coupled this functional has to be invertible, if there is a drive-response configuration the drive determines the evolution of the response, and Φ does not need to be invertible. Identical synchronization is the particular case of generalized synchronization when Φ is the identity.
Read more about this topic: Synchronization Of Chaos
Famous quotes containing the word generalized:
“One is conscious of no brave and noble earnestness in it, of no generalized passion for intellectual and spiritual adventure, of no organized determination to think things out. What is there is a highly self-conscious and insipid correctness, a bloodless respectability submergence of matter in mannerin brief, what is there is the feeble, uninspiring quality of German painting and English music.”
—H.L. (Henry Lewis)