A fully qualified four-wing four-dimensional autonomous chaotic system and its synchronization

Abstract In order to generate a real four-wing chaotic attractor, a new four-dimensional (4D) smooth quadratic autonomous system which is constructed by a linear controller to a three-dimensional (3D) pseudo four-wing system is proposed in this paper. Some complex dynamical behaviors such as equilibrium points and chaos are investigated and analyzed. The corresponding four-wing chaotic attractor is first numerically verified through investigating phase trajectories, Lyapunove exponents, bifurcation diagram, analysis of power spectrum and Poincare maps. Furthermore, an oscillator circuit is designed for implementation, with Multisim observations for verification and demonstration. Finally, an extended synchronization approach is proposed for synchronizing the four-wing chaotic system. On the basis of Jacobin matrix method, it is not necessary to construct the Lyapunov functions, which makes this scheme simpler. Theoretical analysis and numerical simulations demonstrate the validity and feasibility of the proposed control method.

[1]  Chengqing Li,et al.  ARM-embedded implementation of a video chaotic secure communication via WAN remote transmission with desirable security and frame rate , 2016 .

[2]  Li Sheng,et al.  Delay-dependent H∞ synchronization for chaotic neural networks with network-induced delays and packet dropouts , 2016, Neurocomputing.

[3]  Xingming Sun,et al.  Effective and Efficient Global Context Verification for Image Copy Detection , 2017, IEEE Transactions on Information Forensics and Security.

[4]  Marcio Eisencraft,et al.  A digital bandlimited chaos-based communication system , 2016, Commun. Nonlinear Sci. Numer. Simul..

[5]  Yu Si-Min,et al.  Design and implementation of a novel multi-scroll chaotic system , 2009 .

[6]  Shouming Zhong,et al.  On the novel chaotic secure communication scheme design , 2016, Commun. Nonlinear Sci. Numer. Simul..

[7]  Peng Shi,et al.  A new robust adaptive control method for modified function projective synchronization with unknown bounded parametric uncertainties and external disturbances , 2016 .

[8]  Yılmaz Uyaroğlu,et al.  Synchronizations and secure communication applications of a third degree Malasoma system with chaotic flow , 2016 .

[9]  Wenbo Liu,et al.  Dynamical Analysis of a Chaotic System with Two Double-scroll Chaotic attractors , 2004, Int. J. Bifurc. Chaos.

[10]  A. N. Njah,et al.  Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques , 2010 .

[11]  Zhou Ping,et al.  A hyperchaos system with only one nonlinear term , 2009 .

[12]  RANCHAO WU,et al.  Q-S synchronization of the fractional-order unified system , 2013 .

[13]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[14]  GUANRONG CHEN,et al.  Can a Three-Dimensional Smooth Autonomous Quadratic Chaotic System Generate a Single Four-scroll Attractor? , 2004, Int. J. Bifurc. Chaos.

[15]  Barend Jacobus van Wyk,et al.  A four-wing attractor and its analysis , 2009 .

[16]  Zhihua Xia,et al.  A Privacy-Preserving and Copy-Deterrence Content-Based Image Retrieval Scheme in Cloud Computing , 2016, IEEE Transactions on Information Forensics and Security.

[17]  Guanrong Chen,et al.  Theoretical Design and Circuit Implementation of Multidirectional Multi-Torus Chaotic Attractors , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  Chongxin Liu.  A novel chaotic attractor , 2009 .

[19]  Jun-an Lu,et al.  Projectively lag synchronization and uncertain parameters identification of a new hyperchaotic system , 2010 .

[20]  Wang Xing-Yuan,et al.  Hyperchaotic Lorenz system , 2007 .

[21]  Fei Yu,et al.  Secure communication based on a four-wing chaotic system subject to disturbance inputs , 2014 .

[22]  Guo Hui-Jun,et al.  Synchronization of different chaotic systems via active radial basis functions sliding mode controller , 2008 .

[23]  Yao-Chen Hung,et al.  Synchronization of two different systems by using generalized active control , 2002 .

[24]  Chengsheng Yuan,et al.  Fingerprint liveness detection based on multi-scale LPQ and PCA , 2016, China Communications.

[25]  Malek Ghanes,et al.  Passive and impulsive synchronization of a new four-dimensional chaotic system , 2011 .