The nonlinear interaction of two coupled lattice dynamical systems is investigated. It results in identical synchronization when the two coupled lattice systems are same and in generalized synchronization when the parameters are different or the two coupled lattice systems are different. The largest Lyapunov exponent spectra are calculated.

A novel approach is proposed for synchronizing hyperchaotic systems. It is achieved by adjusting the parameters of response system. The variation of parameter can be determined by using of the Routh-Hurwitz stability criterion. As a general method of synchronization, it is robust against external noise.

A further study to a one-dimensional CI transition model is given.The period of the external potential D has a critical value Dc.The phase diagram in the case of D < c is greatly different from that in the case of D > c.When D < c,the phase diagram varies with D and exhibits Farey tree structure in most region of D.When D > c,the phase diagram keeps in the same shape and do not satisfy the Farey tree structure.The procedure of phase transition is studied through the effective potential F(u).

Ionization rate of Hydrogen atom in a two-color laser field is calculated by using the method developed by Kulander etc.Change of ionization rate-phase relation is found when the field intensity goes up to threshold and comparison with classical calculation has been done.

A generalized FK model is presented for treating phase transition problem with double-well interatomic interactions and a perturbed sinusoidal external potential,in which the interatomic interaction is of realistic significance.The effective potential method is used to study its phase diagram and a series of novel,complex but regular phase structures have been found.

A method for contolling chaos in one dimensinal (1-D)maps using periodic perturbation is presented.For a symbolic dynamics givers,the amplitude can be predetermined by means of inverse iterations of the critical point of the map.Properties of the method are illustrated numerically with logistic maps.

The second order Jacobian J₂ is calculated to determine the delay time T of two-dimensional reconstruction about ordinary differential equation according to the first extreme value of J₂.This method gives more information of reconstruction than orhter methods.As an example,the forced Brusselator system is discussed.

Space cells are divided by equal distance step for calculating mutual information, and delay time. This approach is simpler than that of equal probability method. Numerical results indicate that this method can determine the correct delay time, and yield the reconstructed states in the case of forced brusselator.

The problem of optical field chaos in a storage ring free-electron laser oscillator has been discussed by using a phenomenal model. From the theoritical analysis and numerical simulation, it can be found that the chaotic transition of the system via perioddoubling bifurcation still exists when there is a pulsed gain modulation, instead of an oscillated one, in the optical cavity. The existence of optical field chaos has been confirmed by calculating the corresponding value of the leading Lyapunov characteristic exponent. A further research shows that the real form of gain modulation in the optical cavity is most likely a pulsed one, not an oscillated one.

The problem of optical field chaos in a storage ring free-electron laser oscillator hasbeen discussed, by using a phenomenal model. From the theoritical analysis and numerical simulation, it can be found that the variation of laser intensity versus time can be both periodical and chaotic when there is a weak gain modulation in the optical cavity. The correspondent leading Lyapunov characteristic exponent goes to a negative and a positive real number as time increases. Afurther research is carried out, and a chaotic transition via period-doubling bifurcation has been found by varing the modulation parameters.