Lm. Pecora, SYNCHRONIZATION CONDITIONS AND DESYNCHRONIZING PATTERNS IN COUPLED LIMIT-CYCLE AND CHAOTIC SYSTEMS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 58(1), 1998, pp. 347-360
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
.