The topological properties of the delay-time reconstruction transformation of the forced Brusselator system are analysed by means of the Jacobian of the transformation. Topological properties depending on the delay time and on the conditional stability of a time series itself are discussed. The conditional Lyapunov exponent is used to judge whether a time series is good or bad. Results show that the choice of the embedding dimension by using saturation of system invariants is not appropriate.

In this paper a kind of Finite Analytic Methods is derived and applied on convection-diffusion equations. These qualities proved are existence, uniqueness, absolute stability and convergence of solutions of finite analytic scheme of linear equations, so are existence, uniqueness and generalized weak stabability of solutions of finite analytic scheme of Burger's equation. Numerical experiments show that the finite analytic scheme is very effective, especially numerical solutions arc not oscillating.