Si'lnikov chaos in the generalized Lorenz canonical form of dynamical systems

This paper studies the generalized Lorenz canonical form of dynamical systems introduced by. Celikovsky and Chen [ International Journal of Bifurcation and Chaos 12( 8), 2002, 1789]. It proves the existence of a heteroclinic orbit of the canonical form and the convergence of the corresponding series expansion. The. Si'lnikov criterion along with some technical conditions guarantee that the canonical form has Smale horseshoes and horseshoe chaos. As a consequence, it also proves that both the classical Lorenz system and the Chen system have. Si'lnikov chaos. When the system is changed into another ordinary differential equation through a nonsingular one-parameter linear transformation, the exact range of existence of. Si'lnikov chaos with respect to the parameter can be specified. Numerical simulation verifies the theoretical results and analysis.