A constant periodic pulse method for controlling chaos which makes the stable segment of the chaotic orbit form a closed orbit by acting periodic pulses on the system variables is proposed on the basis of the finite time Lyapunov exponents. This method is applied to a high dimensional system with two coupled standard maps. In addition to the results obtained in the low dimensional systems, the stabilized periodic orbit whose period is a multiple of the pulse interval is also found. This is one of the characters of the periodic pulse method. This method is robust under the presence of weak external noise.

It generalizes the Frenkel-Kontorova model to the Frenkel-Kontorova-Devonshire model where the interactions are the triple-well potential. By use of the effective potential method, numerical solutions of eigenvalue problem are used to work out the exact phase diagrams of W a triple-well potential and V a piecewise parabolic potential. According to the winding number ω and the rotation number Ω, the periodicity of the phase diagram is analyzed and some complex but regular phase structures are found.

We calculated the attractor dimensions of the forced Brusselator in autonomous form using the Poincare section method in order to reduce the dimension of the phase space concerned by one.This enables the computation of Kolmogoroff capacity dc with limited storage and facilitates the calculation of the Lyapunov dimension d_L · In calculating d_o we used a cell-merging scheme to get a set of N (ε) correspoonding to different ε, s, while the differential equations were being solved only once for a given set of parameter values Both computer time and stora-gewere saved in this way. In theis paper we makeemphasis on the thechnical subtleties encountered in numerical calculation.