Estimating ultimate bound and finding topological horseshoe for a new chaotic system

This paper presents a new three-dimensional autonomous chaotic system with only one positive term. Basic dynamical properties of the new attractor are demonstrated in terms of phase portraits, equilibria, Lyapunov exponents, Poincare mapping, bifurcation diagram. Furthermore, we derive a three-dimensional spheriform ultimate bound and positively invariant set for all the positive values of its parameters a, b, c. At last, the horseshoe chaos in this system is investigated based on the topological theory.