Dynamic Analysis, Circuit Design, and Synchronization of a Novel 6D Memristive Four-Wing Hyperchaotic System with Multiple Coexisting Attractors

In this work, a novel 6D four-wing hyperchaotic system with a line equilibrium based on a flux-controlled memristor model is proposed. The novel system is inspired from an existing 5D four-wing hyperchaotic system introduced by Zarei (2015). Fundamental properties of the novel system are discussed, and its complex behaviors are characterized using phase portraits, Lyapunov exponential spectrum, bifurcation diagram, and spectral entropy. When a suitable set of parameters are chosen, the system exhibits a rich repertoire of dynamic behaviors including double-period bifurcation of the quasiperiod, a single two-wing, and four-wing chaotic attractors. Further analysis of the novel system shows that the multiple coexisting attractors can be observed with different system parameter values and initial values. Moreover, the feasibility of the proposed mathematical model is also presented by using Multisim simulations based on an electronic analog of the model. Finally, the active control method is used to design the appropriate controller to realize the synchronization between the proposed 6D memristive hyperchaotic system and the 6D hyperchaotic Yang system with different structures. The Routh–Hurwitz criterion is used to prove the rationality of the controller, and the feasibility and effectiveness of the proposed synchronization method are proved by numerical simulations.

[1]  Jin Wang,et al.  Multimodel Framework for Indoor Localization Under Mobile Edge Computing Environment , 2019, IEEE Internet of Things Journal.

[2]  Ke Gu,et al.  Efficient traceable ring signature scheme without pairings , 2020, Adv. Math. Commun..

[3]  Amr Tolba,et al.  Reusable Mesh Signature Scheme for Protecting Identity Privacy of IoT Devices , 2020, Sensors.

[4]  Ke Gu,et al.  Traceable attribute-based signature , 2019, J. Inf. Secur. Appl..

[5]  Fei Yu,et al.  A New 4D Four-Wing Memristive Hyperchaotic System: Dynamical Analysis, Electronic Circuit Design, Shape Synchronization and Secure Communication , 2020 .

[6]  Mu Li,et al.  Improved zeroing neural networks for finite time solving nonlinear equations , 2019, Neural Computing and Applications.

[7]  Fei Yu,et al.  A 2.7 GHz Low-Phase-Noise LC-QVCO Using the Gate-Modulated Coupling Technique , 2016, Wirel. Pers. Commun..

[8]  Ling Zhou,et al.  A novel no‐equilibrium hyperchaotic multi‐wing system via introducing memristor , 2018, Int. J. Circuit Theory Appl..

[9]  Fei Peng,et al.  Identifying natural images and computer generated graphics based on binary similarity measures of PRNU , 2017, Multimedia Tools and Applications.

[10]  Lv Zhao,et al.  Low Voltage Low Power Fully Integrated Chaos Generator , 2018, J. Circuits Syst. Comput..

[11]  Kehui Sun,et al.  Complexity in the muscular blood vessel model with variable fractional derivative and external disturbances , 2019, Physica A: Statistical Mechanics and its Applications.

[12]  Victor S. Sheng,et al.  A convolutional neural network-based linguistic steganalysis for synonym substitution steganography. , 2019, Mathematical biosciences and engineering : MBE.

[13]  徐浩,et al.  Novel four-dimensional autonomous chaotic system generating one-, two-, three- and four-wing attractors , 2011 .

[14]  D. Stewart,et al.  The missing memristor found , 2008, Nature.

[15]  Fang Wang,et al.  Neural network-based finite-time control of quantized stochastic nonlinear systems , 2019, Neurocomputing.

[16]  Yuantao Chen,et al.  The fire recognition algorithm using dynamic feature fusion and IV-SVM classifier , 2019, Cluster Computing.

[17]  Jin Wang,et al.  Complexity and Algorithms for Superposed Data Uploading Problem in Networks With Smart Devices , 2020, IEEE Internet of Things Journal.

[18]  Andrey V. Dmitriev,et al.  Complexity of a Microblogging Social Network in the Framework of Modern Nonlinear Science , 2018, Complex..

[19]  Xi Chen,et al.  Single-Image Super-Resolution Algorithm Based on Structural Self-Similarity and Deformation Block Features , 2019, IEEE Access.

[20]  Kenli Li,et al.  A robust and fixed-time zeroing neural dynamics for computing time-variant nonlinear equation using a novel nonlinear activation function , 2019, Neurocomputing.

[21]  Sundarapandian Vaidyanathan,et al.  Memory Circuit Elements: Complexity, Complex Systems, and Applications , 2019, Complex..

[22]  Cong Xu,et al.  An image encryption algorithm based on a hidden attractor chaos system and the Knuth–Durstenfeld algorithm , 2020, Optics and Lasers in Engineering.

[23]  Lixiang Li,et al.  Chaos-Based Application of a Novel Multistable 5D Memristive Hyperchaotic System with Coexisting Multiple Attractors , 2020, Complex..

[24]  Chunhua Wang,et al.  A universal emulator for memristor, memcapacitor, and meminductor and its chaotic circuit. , 2019, Chaos.

[25]  Chunhua Wang,et al.  Influences of electromagnetic radiation distribution on chaotic dynamics of a neural network , 2020, Appl. Math. Comput..

[26]  Maysoon M. Aziz,et al.  Chaos Control and Synchronization of a Novel 5D Hyperchaotic Lorenz System via Nonlinear Control , 2016 .

[27]  Fei Yu,et al.  A Robust Synchronization-Based Chaotic Secure Communication Scheme With Double-Layered and Multiple Hybrid Networks , 2020, IEEE Systems Journal.

[28]  Ruy Barboza.  Dynamics of a hyperchaotic Lorenz System , 2007, Int. J. Bifurc. Chaos.

[29]  Quan Xu,et al.  A Survey on True Random Number Generators Based on Chaos , 2019, Discrete Dynamics in Nature and Society.

[30]  Fei Tan,et al.  A chaotic secure communication scheme based on synchronization of double-layered and multiple complex networks , 2019, Nonlinear Dynamics.

[31]  Guangyi Wang,et al.  A new modified hyperchaotic Lü system , 2006 .

[32]  Salwa K. Abd-El-Hafiz,et al.  Generalized Dynamic Switched Synchronization between Combinations of Fractional-Order Chaotic Systems , 2017, Complex..

[33]  Ling Zhou,et al.  A Memristive Hyperchaotic Multiscroll Jerk System with Controllable Scroll Numbers , 2017, Int. J. Bifurc. Chaos.

[34]  Hairong Lin,et al.  Chaotic system with bondorbital attractors , 2019, Nonlinear Dynamics.

[35]  Ling Zhou,et al.  The Design and Realization of a Hyper-Chaotic Circuit Based on a Flux-Controlled Memristor with Linear Memductance , 2018, J. Circuits Syst. Comput..

[36]  Wang Xing-Yuan,et al.  Chaos synchronization of the new hyperchaotic Chen system via nonlinear control , 2006 .

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

[38]  Jinde Cao,et al.  Hybrid multisynchronization of coupled multistable memristive neural networks with time delays , 2019, Neurocomputing.

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

[40]  F. Yu,et al.  Antisynchronization of a novel hyperchaotic system with parameter mismatch and external disturbances , 2012 .

[41]  Guoyuan Qi,et al.  A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system , 2010 .

[42]  Sundarapandian Vaidyanathan,et al.  Hyperchaos, adaptive control and synchronization of a novel 5-D hyperchaotic system with three positive Lyapunov exponents and its SPICE implementation , 2014 .

[43]  Chunhua Wang,et al.  Multi-scroll hidden attractors with two stable equilibrium points. , 2019, Chaos.

[44]  L. Chua.  Memristor-The missing circuit element , 1971 .

[45]  Sundarapandian Vaidyanathan,et al.  Fractional-Order and Memristive Nonlinear Systems: Advances and Applications , 2017, Complex..

[46]  Fei Yu,et al.  Grid Multiscroll Hyperchaotic Attractors Based on Colpitts Oscillator Mode with Controllable Grid Gradient and Scroll Numbers , 2013 .

[47]  Lei Gao,et al.  A fully qualified four-wing four-dimensional autonomous chaotic system and its synchronization , 2017 .

[48]  Jie Jin,et al.  Fully Integrated Memristor and Its Application on the Scroll-Controllable Hyperchaotic System , 2019, Complex..

[49]  Xu Zhang,et al.  Hidden extreme multistability in a novel 4D fractional-order chaotic system , 2019 .

[50]  Leon O. Chua,et al.  Memristor oscillators , 2008, Int. J. Bifurc. Chaos.

[51]  Kehui Sun,et al.  Dynamics of a higher dimensional fractional-order chaotic map , 2019, Physica A: Statistical Mechanics and its Applications.

[52]  Jie Jin,et al.  Programmable multi-direction fully integrated chaotic oscillator , 2018, Microelectron. J..

[53]  Jin Wang,et al.  RETRACTED ARTICLE: The visual object tracking algorithm research based on adaptive combination kernel , 2019, Journal of Ambient Intelligence and Humanized Computing.

[54]  Ke Gu,et al.  Secure Data Query Framework for Cloud and Fog Computing , 2020, IEEE Transactions on Network and Service Management.

[55]  Junwei Lu,et al.  Fixed-time continuous stochastic synchronisation of two-layer dynamical networks , 2020, Int. J. Syst. Sci..

[56]  Lili Zhou,et al.  Generating hyperchaotic multi-wing attractor in a 4D memristive circuit , 2016, Nonlinear Dynamics.

[57]  Fei Yu,et al.  A 1 V, 0.53 ns, 59 μW Current Comparator Using Standard 0.18 μm CMOS Technology , 2020, Wirel. Pers. Commun..

[58]  Chunhua Wang,et al.  A Novel Multi-Attractor Period Multi-Scroll Chaotic Integrated Circuit Based on CMOS Wide Adjustable CCCII , 2019, IEEE Access.

[59]  Yun Song,et al.  Complete Switched Generalized Function Projective Synchronization of a Class of Hyperchaotic Systems With Unknown Parameters and Disturbance Inputs , 2014 .

[60]  Fei Yu,et al.  Cluster synchronization of two-layer nonlinearly coupled multiplex networks with multi-links and time-delays , 2019, Neurocomputing.

[61]  Hee-Jun Kang,et al.  Fixed-Time Complex Modified Function Projective Lag Synchronization of Chaotic (Hyperchaotic) Complex Systems , 2017, Complex..

[62]  Malek Ghanes,et al.  A Novel 5D-Dimentional Hyperchaotic System and its Circuit Simulation by EWB , 2015 .

[63]  Qigui Yang,et al.  A New 6D Hyperchaotic System with Four Positive Lyapunov Exponents Coined , 2015, Int. J. Bifurc. Chaos.

[64]  Fei Peng,et al.  Separable reversible data hiding and encryption for HEVC video , 2017, Journal of Real-Time Image Processing.

[65]  Yu Fei,et al.  Time-controllable projective synchronization of a class of chaotic systems based on adaptive method , 2013 .

[66]  J. Li,et al.  Heteroclinic Chaotic Threshold in a Nonsmooth System with Jump Discontinuities , 2020, Int. J. Bifurc. Chaos.

[67]  Chunhua Wang,et al.  A Novel Color Image Encryption Algorithm Based on Hyperchaotic System and Permutation-Diffusion Architecture , 2019, Int. J. Bifurc. Chaos.

[68]  Fei Yu,et al.  A Low-Voltage and Low-Power 3-GHz CMOS LC VCO for S-Band Wireless Applications , 2014, Wireless Personal Communications.

[69]  Anaclet Fomethe,et al.  A novel memristive 6D hyperchaotic autonomous system with hidden extreme multistability , 2019, Chaos, Solitons & Fractals.

[70]  Li Liu,et al.  Design and FPGA Implementation of a Pseudorandom Number Generator Based on a Four-Wing Memristive Hyperchaotic System and Bernoulli Map , 2019, IEEE Access.

[71]  Olfa Boubaker,et al.  Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms , 2017, Complex..

[72]  Ping Li,et al.  Research progress of multi-scroll chaotic oscillators based on current-mode devices , 2016 .

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

[74]  Chunhua Wang,et al.  Multi-piecewise quadratic nonlinearity memristor and its 2N-scroll and 2N + 1-scroll chaotic attractors system. , 2017, Chaos.

[75]  Hui Shen,et al.  CCII and FPGA Realization: A Multistable Modified Fourth-Order Autonomous Chua's Chaotic System with Coexisting Multiple Attractors , 2020, Complex..

[76]  Haijun Wang,et al.  New dynamics coined in a 4-D quadratic autonomous hyper-chaotic system , 2019, Appl. Math. Comput..

[77]  Amin Zarei,et al.  Complex dynamics in a 5-D hyper-chaotic attractor with four-wing, one equilibrium and multiple chaotic attractors , 2015 .

[78]  Louis M Pecora,et al.  Synchronization of chaotic systems. , 2015, Chaos.

[79]  Chunhua Wang,et al.  A New Chaotic Image Encryption Scheme Using Breadth-First Search and Dynamic Diffusion , 2018, Int. J. Bifurc. Chaos.

[80]  Jong Hyuk Park,et al.  Parameterized algorithms of fundamental NP-hard problems: a survey , 2020, Human-centric Computing and Information Sciences.

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

[82]  Fei Yu,et al.  Analysis and FPGA Realization of a Novel 5D Hyperchaotic Four-Wing Memristive System, Active Control Synchronization, and Secure Communication Application , 2019, Complex..

[83]  Hui Shen,et al.  Secure Communication Scheme Based on a New 5D Multistable Four-Wing Memristive Hyperchaotic System with Disturbance Inputs , 2020, Complex..

[84]  Hu Yan,et al.  Projective synchronization of a five-term hyperbolic-type chaotic system with fully uncertain parameters , 2012 .

[85]  Ling Zhou,et al.  Generating Four-Wing Hyperchaotic Attractor and Two-Wing, Three-Wing, and Four-Wing Chaotic Attractors in 4D Memristive System , 2017, Int. J. Bifurc. Chaos.