Research Article A New No-Equilibrium Chaotic System and Its Topological Horseshoe Chaos Chunmei Wang, 1 Chunhua Hu, 2 Jingwei Han, 3 and Shijian Cang 4,5 1 Department of Information Engineering, Binzhou University, Binzhou 256600, China 2 Department of Electrical Engineering, Binzhou University, Binzhou 256600, China 3 College of Aeronautical Engineering, Binzhou University, Binzhou 256600, China 4 Department of Product Design, Tianjin University of Science and Technology, Tianjin 300457, China 5 School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China Correspondence should be addressed to Shijian Cang; sj.cang@gmail.com Received 13 September 2016; Revised 11 November 2016; Accepted 6 December 2016 Academic Editor: Xavier Leoncini Copyright © 2016 Chunmei Wang et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A new no-equilibrium chaotic system is reported in this paper. Numerical simulation techniques, including phase portraits and Lyapunov exponents, are used to investigate its basic dynamical behavior. To confrm the chaotic behavior of this system, the existence of topological horseshoe is proven via the Poincar´ e map and topological horseshoe theory. 1. Introduction Since Lorenz found an atmosphere dynamical model which can generate butterfy-shaped chaotic attractor in 1963 [1], chaos theory in the past fve decades has attracted a lot of attention and hence triggered the emergence of a huge literature in this area. Since then, many kinds of chaotic or hyperchaotic systems governed by nonlinear ordinary diferential equations (ODEs), including autonomous and nonautonomous chaotic systems [2–4], continuous and dis- crete chaotic systems [5–7], integer-order and fractional- order chaotic systems [1, 2, 7, 8], and chaotic systems with self-excited attractor and hidden attractor [9–11], were developed, and continuous chaotic systems governed by nonlinear partial diferential equations (PDEs) [12–14] were also investigated. To our knowledge, we summarize four criteria for the existence of chaos in the investigation of dynamical systems. Te frst one is the well-known Lyapunov exponents [15]. If there is at least one positive Lyapunov exponent in a dynamical system, the dynamics of this system is chaotic. Te second one is Sil’nikov’s criterion for the existence of chaos [16, 17]. Te main steps are as follows: (1) calculate equilibrium points of a dynamical system; (2) fnd a homo- clinic or heteroclinic orbit connecting equilibrium points by using the undetermined coefcient method; and (3) prove the convergence of the homoclinic or heteroclinic orbit series expansion obtained before. If the convergence can be proved, horseshoe chaos occurs. Te third one is Melnikov’s criterion which is a powerful approximate tool for investigating chaos occurrence in near Hamiltonian systems and has been suc- cessfully applied to the analysis of chaos in smooth systems by calculating the distance between the stable and unstable manifold [18]. For dynamical systems, when the stable and unstable manifolds of their fxed points in the Poincar´ e map intersect transversely for sufciently small parameter, there exists chaos in the sense of Smale horseshoe. Te last one is the topological horseshoes theory which is based on the geometry of continuous maps on some subsets of interest in state space [19–23]. It is more applicable for computer- assisted verifcations for the existence of chaotic behavior in dynamical systems in theory. A comparative analysis of these methods shows that the calculation of Lyapunov exponents and the topological horseshoes theory can be widely applied, but the Sil’nikov criterion is suitable for these systems where there is a homoclinic or heteroclinic orbit. Obviously, the Sil’nikov criterion cannot be used in no-equilibrium systems. Very recently, hidden attractor in dynamical systems has been an important research topic because it has properties diferent from self-excited attractor. An attractor is called the Hindawi Publishing Corporation Advances in Mathematical Physics Volume 2016, Article ID 3142068, 6 pages http://dx.doi.org/10.1155/2016/3142068