Analysis of the Phaseportrait for the Lü Dynamical System in a Particular Case


In the present paper it is started a qualitative analysis of the Lü dynamical system, using the appropiate tools of Hamilton-Poisson geometry and using the software for mathematics MAPLE 15. The Lü’s system arise from electrical engineering networks and it is very known that he has a chaotic behavior. For this reason, the problem of finding the solution of the system could be very difficult. By obtaining of a geometric Hamilton-Poisson structure, we can find such a solution as the intersection of two surfaces, the surfaces equation being given by the Hamiltonian and the Casimir function . Using MAPLE 15, it will be analyzed the phase portrait for two particular simplified versions of the dynamical system associated to the Lü ordinary differential system (a=0, b=c=0 and a=1, b=c=0). Also, we will do a study of the Lyapunov stability of Lü’s system for the particular case (a=1, b=c=0). We obtain that the origin is an unstable equilibrium point for this particular parameter case of the Lü’s model. This fact is confirmed by the numerical simulations. More that, the pictures show that the origin is a non-stable focus, in the first simulation case. Analytical results are accompanied by numerical illustrations. images