A Chaotic System With One Saddle and Two Stable Node-Foci

Abstract

This paper reports the finding of a chaotic system with one saddle and two stable node-foci in a simple three-dimensional (3D) autonomous system. The system connects the original Lorenz system and the original Chen system and represents a transition from one to the other. The algebraical form of the chaotic attractor is very similar to the Lorenz-type systems but they are different and, in fact, nonequivalent in topological structures. Of particular interest is the fact that the chaotic system has a chaotic attractor, one saddle and two stable node-foci. To further understand the complex dynamics of the system, some basic properties such as Lyapunov exponents, bifurcations, routes to chaos, periodic windows, possible chaotic and periodic-window parameter regions, and the compound structure of the system are analyzed and demonstrated with careful numerical simulations.

A Novel Image Encryption Scheme Based on Self-Synchronous Chaotic Stream Cipher and Wavelet Transform

“…However, because of the high correlation and redundancy of adjacent pixels of the digital image, some international standard encryption algorithms are not suitable for image encryption, including 3DES (Triple Data Encryption Algorithm), IDEA (International Data Encryption Algorithm), and AES (Advanced Encryption Standard), etc. On the other hand, the chaotic nonlinear dynamic system has some good characteristics, such as positive Lyapunov exponents, ergodicity, sensitivity to initial conditions, topological transitivity, and unpredictability [2][3][4][5], and was widely applied in the field of cryptography and secret communication.…”

Periodic parametric perturbation control for a 3D autonomous chaotic system and its dynamics at infinity

“…In fact, the DOI: 10.14736/kyb-2017-2-0354 transition system (Yang-Chen system group) has been discussed by Gh. Tigan, Yang and Wang in 2005, 2008, 2010 respectively [20,23,25,33]. Since the transition chaotic system connects the Lorenz attractor and Chen attractor, how to construct a transition system will be an important thing in chaos research.…”

Dynamics analysis and robust modified function projective synchronization of Sprott E system with quadratic perturbation

“…Based on a classification condition formulated by Vaněček andČelikovský [21], these chaotic systems satisfy a 12 a 21 > 0, a 12 a 21 < 0, or a 12 a 21 = 0. Moreover, according to the classification developed in [26], they are classified into the Lorenz system group if a 11 a 12 < 0, the Chen system group if a 11 a 12 < 0, or the Yang-Chen system (transition system) group if a 11 a 12 = 0. Most of the studied chaotic systems belong to the Shilnikov type, but the Shilnikov criteria is not sufficient-necessary condition for emergence of chaos.…”