Si´lnikov Heterclinic Orbits of a New Chaos

A new chaotic attractor is discovered. The heteroclinic orbits in the new system has been found by using the undermined coefficient method. It analytically demonstrates that there exists one heteroclinic orbit of the Si´lnikov type that connects two nontrivial equilibrium points, and therefore Smale horseshoes and the horsesheos chaos occur for this system via the Si´likov criterion. The convergence of the series of expansions of the two types of orbits is proved.