Dynamics at infinity and the existence of singularly degenerate heteroclinic cycles in the conjugate Lorenz-type system

In this paper, by using the Poincaré compactification in R3R3, a global analysis of the conjugate Lorenz-type system is presented, including the complete description of its dynamic behavior on the sphere at infinity. Combining analytical and numerical techniques, it is shown that for the parameter value b=0b=0 the system presents an infinite set of singularly degenerate heteroclinic cycles. The chaotic attractors for the system in the case of small b>0b>0 are found numerically, and thus the nearby singularly degenerate heteroclinic cycles. It is hoped that this global study can give a contribution in understanding of the conjugate Lorenz-type system, and will shed some light leading to final revelation of the true geometrical structure and the essence of chaos for the amazing original Lorenz attractor.