The Smale horseshoe-type chaos in the general 3-D quadratic continuous-time system with a cubic term

Abstract

This paper presents the existence of horseshoe-type chaos in the general 3-D quadratic continuous-time system with a cubic term. For the discussion of chaos, the bifurcate parameter value is limited to the requirement of the Shilnikov theorem. Also, The existence of the homoclinic orbit has been proven by using the undetermined coefficient method. Finally, an example is provided to illustrate the main result.