Directed collective motion in a circular array of unidirectionally coupled oscillators with symmetric potential is obtained numerically in the absence of external bias. This striking feature is interpreted as the effect of the spontaneous breaking of temporal symmetry of the coupling. It is revealed that a proper match of various control parameters is important in generating an optimal coherent global transport. Noise-sustained directed transport is also observed, and the related stochastic resonance in an autonomous system is identified..

Generalized synchronization in an array of mutually (bidirectionally) coupled nonidentical chaotic oscillators is studied. Coupled Lorenz oscillators and coupled Lorenz-Rossler oscillators are adopted as our working models. With increasing the coupling strengths, the system experiences a cascade of transitions from the partial to the global generalized synchronizations, i.e., different oscillators are gradually entrained through a clustering process. This scenario of transitions reveals an intrinsic self-organized order in groups of interacting units, which generalizes the idea of generalized synchronizations in drive-response systems.

Irreversible processes of few hard-ball (N) mechanical systems are investigated numerically and compared with the theoretical results of quasistatic processes. The thermodynamic second law is valid for N≥2 for both equilibrium and nonequilibrium systems if the average ensemble of the large number of identical systems is taken.

The relation between generalized synchronization and phase synchronization is investigated. It was claimed that generalized synchronization always leads to phase synchronization, and phase synchronization is a weaker form than generalized synchronization. We propose examples that generalized synchronization can be weaker than phase synchronization, depending on parameter misfits. Moreover, generalized synchronization does not always lead to phase synchronization.

The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the phase-locking state, simultaneous phase slips of all oscillators and quantized phase shifts in these phase slips are observed. By increasing the coupling, a bifurcation tree from high-dimensional quasiperiodicity to chaos to quasiperiodicity and periodicity is found. Different orders of phase synchronizations of chaotic oscillators and chaotic clusters play the key role for constructing this tree structure.