Design and circuit implementation of a five‐dimensional hyperchaotic system with linear parameter

Based on an existing 4‐dimensional Lorenz hyperchaotic system, a novel 5‐dimensional hyperchaotic system is proposed by an extra linear control coefficient in this paper. Some related characters are analysed comprehensively, including the stability of equilibrium, dissipativity, rotation symmetry, bifurcations, Lyapunov exponent, and Poincare surface of a section of the hyperchaotic system. The 5‐dimensional hyperchaotic system is then implemented and simulated in the circuit simulation software NI Multisim. The results indicate that the proposed hyperchaotic system exhibits hyperchaos, chaos, and quasi‐periodic and periodic dynamic behaviours, which can facilitate and enhance the security of chaos‐based communication.

[1]  Zhisheng Duan,et al.  Leader-Following Consensus of Multi-Agent Systems With Switching Networks and Event-Triggered Control , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[2]  Yicong Zhou,et al.  Designing Hyperchaotic Cat Maps With Any Desired Number of Positive Lyapunov Exponents , 2018, IEEE Transactions on Cybernetics.

[3]  Wei Zhang,et al.  Hidden hyperchaos and electronic circuit application in a 5D self-exciting homopolar disc dynamo. , 2017, Chaos.

[4]  Dongdong Lin,et al.  Cryptanalyzing an Image-Scrambling Encryption Algorithm of Pixel Bits , 2016, IEEE MultiMedia.

[5]  Viet-Thanh Pham,et al.  A Novel Four-Dimensional Hyperchaotic Four-Wing System With a Saddle–Focus Equilibrium , 2016, IEEE Transactions on Circuits and Systems II: Express Briefs.

[6]  S. Vaidyanathan.  Hyperchaos, adaptive control and synchronization of a novel 4-D hyperchaotic system with two quadratic nonlinearities , 2016 .

[7]  Mou Jun,et al.  Memristor-based Lorenz hyper-chaotic system and its circuit implementation , 2016 .

[8]  Jacques M. Bahi,et al.  Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems , 2015, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Chao Bai,et al.  Secure communication based on spatiotemporal chaos , 2015 .

[10]  Yigang He,et al.  A New Chaotic Attractor and Its Synchronization Implementation , 2015, Circuits Syst. Signal Process..

[11]  Guang Zeng,et al.  Hyperchaos and horseshoe in a 4D memristive system with a line of equilibria and its implementation , 2014, Int. J. Circuit Theory Appl..

[12]  Julien Clinton Sprott,et al.  A New Piecewise Linear Hyperchaotic Circuit , 2014, IEEE Transactions on Circuits and Systems II: Express Briefs.

[13]  Guanrong Chen,et al.  Designing Hyperchaotic Systems With Any Desired Number of Positive Lyapunov Exponents via A Simple Model , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Manuel Merino,et al.  Chen's attractor exists if Lorenz repulsor exists: the Chen system is a special case of the Lorenz system. , 2013, Chaos.

[15]  Qigui Yang,et al.  A 5D hyperchaotic System with Three positive Lyapunov exponents Coined , 2013, Int. J. Bifurc. Chaos.

[16]  Tao Xie,et al.  Breaking a novel image encryption scheme based on improved hyperchaotic sequences , 2012, Nonlinear Dynamics.

[17]  Yuen Ching-Hung,et al.  Chaos-based encryption for fractal image coding , 2012 .

[18]  Luigi Fortuna,et al.  Experimental robust synchronization of hyperchaotic circuits , 2009 .

[19]  Xingyuan Wang,et al.  A hyperchaos generated from Lorenz system , 2008 .

[20]  Guanrong Chen,et al.  Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications , 2006 .

[21]  Xiao-Song Yang,et al.  Chaos and transient chaos in simple Hopfield neural networks , 2005, Neurocomputing.

[22]  Guanrong Chen,et al.  A twin‐star hyperchaotic attractor and its circuit implementation , 2003, Int. J. Circuit Theory Appl..

[23]  A. Tamasevicius,et al.  Hyperchaos in coupled Colpitts oscillators , 2003 .

[24]  Daizhan Cheng,et al.  Bridge the Gap between the Lorenz System and the Chen System , 2002, Int. J. Bifurc. Chaos.

[25]  Silvano Cincotti,et al.  Hyperchaotic behaviour of two bi‐directionally coupled Chua's circuits , 2002, Int. J. Circuit Theory Appl..

[26]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[27]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[28]  O. Rössler.  An equation for hyperchaos , 1979 .

[29]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .