SYNCHRONIZATION CONDITIONS AND DESYNCHRONIZING PATTERNS IN COUPLED LIMIT-CYCLE AND CHAOTIC SYSTEMS

Many coupling schemes for both limit-cycle and chaotic systems involve adding linear combinations of dynamical variables from various oscill ators in an array of identical oscillators to each oscillator node of the array. Examples of such couplings are (nearest neighbor) diffusive coupling, all-to-all coupling, star coupling, and random linear coupl ings. We show that for a given oscillator type and a given choice of o scillator variables to use in the coupling arrangement, the stability of each linear coupling scheme can be calculated from the stability of any other for symmetric coupling schemes. In particular, when there a re desynchronization bifurcations our approach reveals interesting pat terns and relations between desynchronous modes, including the situati on in which for some systems there is a limit on the number of oscilla tors that can be coupled and still retain synchronous chaotic behavior .