Abstract
This article introduces a new chaotic system of three-dimensionalquadratic autonomous ordinary differential equations, which candisplay different attractors with two unstable equilibrium pointsand four unstable equilibrium points respectively. Dynamicalproperties of this system are then studied. Furthermore, by applyingthe undetermined coefficient method, heteroclinic orbit of Shil'nikov's type in this system is found and the convergence of theseries expansions of this heteroclinic orbit are proved in thisarticle. The Shil'nikov's theorem guarantees that this system hasSmale horseshoes and the horseshoe chaos.
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