Existence of a new three-dimensional chaotic attractor

In this paper, one heteroclinic orbit of a new three-dimensional continuous autonomous chaotic system, whose chaotic attractor belongs to the conjugate Lü attractor, is found. The series expression of the heteroclinic orbit of Šhil’nikov type is derived by using the undetermined coefficient method. The uniform convergence of the precise series expansions of this heteroclinic orbits is proved. According to the Šhil’nikov theorem, this system clearly has Smale horseshoes and the horseshoe chaos.