Dynamical behaviours of the motion of particles in a periodic potential under a constant driving velocity by a spring at one end are explored. In the stationary case, the stable equilibrium position of the particle experiences an elasticity instability transition. When the driving velocity is nonzero, depending on the elasticity coefficient and the pulling velocity, the system exhibits complicated and interesting dynamics, such as periodic and chaotic motions. The results obtained here may shed light on studies of dynamical processes in sliding friction.
We investigate the wavefronts depinning in current biased, infinitely long semiconductor superlattice systems by the method of discrete mapping and show that the wavefront depinning corresponds to the discrete mapping failure. For parameter values near the lower critical current in both discrete drift model （DD model） and discrete drift-diffusion model （DDD model）, the mapping failure is determined by the important mapping step from the bottom of branch to branch α. For the upper critical parameters in DDD model, the key mapping step is from branch γ to the top of the corresponding branch α and we may need several active wells to describe the wavefronts.
The usual linear variable feedback control method is extended to a generalized function feedback scheme. The scheme is applied to high-dimensional spatiotemporal systems. By a combination of local generlized feedback control and the spatial coupling effect among elements, turbulent motion can be successfully eliminated.
