SYNCHRONIZATION OF SYMMETRICAL CHAOTIC SYSTEMS

This paper contains a study of the synchronization by homogeneous nonl inear driving of systems that are symmetric in phase space. The main c onsequence of this symmetry is the ability of the response to synchron ize in more than just one way to the driving systems. These different forms of synchronization are to be understood as generalized synchroni zation states in which the motions of drive and response are in comple te correlation, but the phase space distance between them does not con verge to zero. In this case the synchronization phenomenon becomes enr iched because there is multistability. As a consequence, there appear multiple basins of attraction and special responses to external noise. It is shown, by means of a computer simulation of various nonlinear s ystems, that: (i) the decay to the generalized synchronization states is exponential, (ii) the basins of attraction are symmetric, usually c omplicated, frequently fractal, and robust under the changes in the pa rameters, and (iii) the effect of external noise is to weaken the sync hronization, and in some cases to produce jumps between the various sy nchronization states available.