Synchronization, anti-synchronization and circuit realization of a novel hyper-chaotic system

Purpose This paper aims to introduce a novel four-dimensional hyper-chaotic system with different hyper-chaotic attractors as certain parameters vary. The typical dynamical behaviors of the new hyper-chaotic system are discussed in detail. The control problem of these hyper-chaotic attractors is also investigated analytically and numerically. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components. Design/methodology/approach The adaptive control method is derived to achieve chaotic synchronization and anti-synchronization of the novel hyper-chaotic system with unknown parameters by making the synchronization and anti-synchronization error systems asymptotically stable at the origin based on Lyapunov stability theory. Then, two novel electronic circuits of the proposed hyper-chaotic system with different parameters are presented and realized using physical components. Multisim simulations and electronic circuit experiments are consistent with MATLAB simulation results and they verify the existence of these hyper-chaotic attractors. Findings Comparisons among MATLAB simulations, Multisim simulation results and physical experimental results show that they are consistent with each other and demonstrate that changing attractors of the hyper-chaotic system exist. Originality/value The goal of this paper is to construct a new four-dimensional hyper-chaotic system with different attractors as certain parameters vary. The adaptive synchronization and anti-synchronization laws of the novel hyper-chaotic system are established based on Lyapunov stability theory. The corresponding electronic circuits for the novel hyper-chaotic system with different attractors are also implemented to illustrate the accuracy and efficiency of chaotic circuit design.

[1]  Jun Tang,et al.  A class of initials-dependent dynamical systems , 2017, Appl. Math. Comput..

[2]  E. Tlelo-Cuautle,et al.  FPGA realization of a chaotic communication system applied to image processing , 2015 .

[3]  José-Cruz Nuñez Pérez,et al.  FPGA realization of multi-scroll chaotic oscillators , 2015, Commun. Nonlinear Sci. Numer. Simul..

[4]  Ana Dalia Pano-Azucena,et al.  Arduino-based chaotic secure communication system using multi-directional multi-scroll chaotic oscillators , 2016, Nonlinear Dynamics.

[5]  Emad E. Mahmoud,et al.  Synchronization and control of hyperchaotic complex Lorenz system , 2010, Math. Comput. Simul..

[6]  Runtong Chu,et al.  Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice , 2014 .

[7]  Zhigang Zeng,et al.  Stability analysis for uncertain switched neural networks with time-varying delay , 2016, Neural Networks.

[8]  V. Sundarapandian,et al.  Analysis, control, synchronization, and circuit design of a novel chaotic system , 2012, Math. Comput. Model..

[9]  Zhigang Zeng,et al.  New results on anti-synchronization of switched neural networks with time-varying delays and lag signals , 2016, Neural Networks.

[10]  Emad E. Mahmoud,et al.  Complete synchronization of chaotic complex nonlinear systems with uncertain parameters , 2010 .

[11]  Ahmed M. A. El-Sayed,et al.  Circuit realization, bifurcations, chaos and hyperchaos in a new 4D system , 2014, Appl. Math. Comput..

[12]  Mohamed Benrejeb,et al.  On observer-based secure communication design using discrete-time hyperchaotic systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[13]  Long Huang,et al.  Parameters estimation, mixed synchronization, and antisynchronization in chaotic systems , 2014, Complex..

[14]  Li Cai,et al.  Novel Hyperchaotic System and Its Circuit Implementation , 2015 .

[15]  Zhigang Zeng,et al.  Controller design for global fixed-time synchronization of delayed neural networks with discontinuous activations , 2017, Neural Networks.

[16]  Emad E. Mahmoud,et al.  Complex complete synchronization of two nonidentical hyperchaotic complex nonlinear systems , 2014 .

[17]  Parag Gupta,et al.  Design and Hardware Implementation of a New Chaotic Secure Communication Technique , 2016, PloS one.

[18]  Mauricio Zapateiro,et al.  A secure communication scheme based on chaotic Duffing oscillators and frequency estimation for the transmission of binary-coded messages , 2014, Commun. Nonlinear Sci. Numer. Simul..

[19]  Jesus M. Munoz-Pacheco,et al.  Frequency limitations in generating multi-scroll chaotic attractors using CFOAs , 2014 .

[20]  M. Boutayeb,et al.  Generalized state-space observers for chaotic synchronization and secure communication , 2002 .

[21]  Emad E. Mahmoud,et al.  ANALYSIS OF HYPERCHAOTIC COMPLEX LORENZ SYSTEMS , 2008 .

[22]  Carlos Sánchez-López,et al.  Integrated circuit generating 3- and 5-scroll attractors , 2012 .

[23]  K. Thamilmaran,et al.  Hyperchaos in SC-CNN based modified canonical Chua’s circuit , 2014 .

[24]  J. Nunez,et al.  CCII+ Based on QFGMOS for Implementing Chua s Chaotic Oscillator , 2015, IEEE Latin America Transactions.

[25]  Hsin-Chieh Chen,et al.  Hardware Implementation of Lorenz Circuit Systems for Secure Chaotic Communication Applications , 2013, Sensors.

[26]  Leon O. Chua,et al.  Simplest Chaotic Circuit , 2010, Int. J. Bifurc. Chaos.

[27]  M. Ghanes,et al.  Circuit Simulation of an Analog Secure Communication based on Synchronized Chaotic Chua's System , 2014 .

[28]  Xinguo Zhang,et al.  Analysis, circuit implementation and applications of a novel chaotic system , 2017 .

[29]  Emad E. Mahmoud,et al.  Dynamics and synchronization of new hyperchaotic complex Lorenz system , 2012, Math. Comput. Model..

[30]  Shuzhi Sam Ge,et al.  Robust Adaptive Control for a Class of MIMO Nonlinear Systems by State and Output Feedback , 2014, IEEE Transactions on Automatic Control.

[31]  Christopher Edwards,et al.  Adaptive Sliding-Mode-Observer-Based Fault Reconstruction for Nonlinear Systems With Parametric Uncertainties , 2008, IEEE Transactions on Industrial Electronics.

[32]  Carlos Sánchez-López,et al.  Multiscroll floating gate–based integrated chaotic oscillator , 2013, Int. J. Circuit Theory Appl..

[33]  Alan V. Oppenheim,et al.  Circuit implementation of synchronized chaos with applications to communications. , 1993, Physical review letters.

[34]  Alan V. Oppenheim,et al.  Synchronization of Lorenz-based chaotic circuits with applications to communications , 1993 .

[35]  Sundarapandian Vaidyanathan,et al.  Analysis, synchronization and circuit design of a novel butterfly attractor , 2014 .

[36]  Tsung-Chih Lin,et al.  Synchronization of Fuzzy Modeling Chaotic Time Delay Memristor-Based Chua’s Circuits with Application to Secure Communication , 2015, Int. J. Fuzzy Syst..