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).

The influences of the second periodic-forced term on the forced Brusselator are discussed.When the frequency of the two forces are commensurable, the system, which is chaos without the second forcing, can be chaos or periodic. If the two frequency are incommensurable, the system appears one mo re new movement state other than chaos and periodic:that is an strange nonchaotic attractor.

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.

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.

In this paper, numerical studes are performed on a model for a coupled standard mapping to investigate the Arnold diffusion. We present estimates diffusion coefficient as a function of coupling constant b, the nonlinearity parameters k and the number of iteration N, and compared with the results of the theoretical. We estimates the diffusion coefficent along the thin stochastic layer of the J-ψ motion. For samll parameter values, theoretical pradiction agrees well with numerical result.