Abstract: The continuation algorithm is applied to calculate the steady and periodic solutions of the 5-dimensional convection nonlinear dynamical system. The real bifurcation points curve, limit points curve and Hopf bifurcation points curve of the model are drawn in the parameter plane Ri-Re. The bifurcation diagram.is obtained. The different type of stable solutions such as stationary attractor, periodic attractor and chaotic attractor and so on exist in the different blocks or regions in the bifurcation diagram. Through analysing the bifurcation course of the steady and periodic solutions curve, the physical transitions both from steady state to periodic state and from periodic state to chaotic state which happened in the atomspheric stratified layer are discussed.The numerical computation results show that the continuation algorithm is a very effective computational method for researching into the bifurcation and dissipative structure of a nonlinear-dynamical system.

Key words: steady solution, periodic solution, chaos, bifurcation, continuation algorithm