Zhang Ruo-Xun( ) a)b) and Yang Shi-Ping( ) a) †

A new stability theory of nonlinear dynamic systems is proposed, and a novel adaptive synchronisation method is presented for fractional-order chaotic and hyperchaotic systems based on the theory described in this paper. In comparison with previous methods, not only is the present control scheme simple but also it employs only one control strength, converges very fast, and it is also suitable for a large class of fractional-order chaotic and hyperchaotic systems. Moreover, this scheme is analytical and simple to implement in practice. Numerical and circuit simulations are used to validate and demonstrate the effectiveness of the method.

This paper studies the nonsequential double ionization (NSDI) process of diatomic molecules aligned parallel and perpendicular to an intense linearly polarized laser field by using a three-dimensional semiclassical model. With this model, it achieves insight into the ion momentum distribution under the combined influence of a two-centre Coulomb potential and an intense laser field, and this result shows the significant influence of molecular alignment on the ratio between double and single ionization rate. Careful investigations show that the NSDI process for different alignment molecules has a close relation to the laser intensity and the different bounding electron distribution has a significant influence on the final ion momentum distribution.

S-matrix study on alignment dependence of single ionization of molecular ions with different active orbitals *Li Yan(李 燕) a) , Jia Xin-Yan(贾欣燕) b) † , Yang Shi-Ping(杨世平) a) ‡ , Li Wei-Dong(李卫东) c) , and Chen Jing(陈 京) b)d)