The influence of connectivity on the global dynamics of nonlinear oscillator ensembles

In this thesis we have studied the global dynamics which spontaneously emerge in ensembles of interacting disparate nonlinear oscillators. Collective phenomena exhibited in these systems include synchronization, quasiperiodicity, chaos, and death. Exact analytical solutions are presented for two and three coupled oscillators with phase and amplitude variations. A phenomenon analogous to a phase-transition is found as a function of interaction-range in a one-dimensional lattice: for coupling exponents larger than some critical value, alpha c, synchronization is shown to be impossible. Massively parallel computer simulations in conjunction with finite-size scaling were used to extrapolate to the infinite-size limit.