Coexisting Attractors and Multistability in a Simple Memristive Wien-Bridge Chaotic Circuit

In this paper, a new voltage-controlled memristor is presented. The mathematical expression of this memristor has an absolute value term, so it is called an absolute voltage-controlled memristor. The proposed memristor is locally active, which is proved by its DC V–I (Voltage–Current) plot. A simple three-order Wien-bridge chaotic circuit without inductor is constructed on the basis of the presented memristor. The dynamical behaviors of the simple chaotic system are analyzed in this paper. The main properties of this system are coexisting attractors and multistability. Furthermore, an analog circuit of this chaotic system is realized by the Multisim software. The multistability of the proposed system can enlarge the key space in encryption, which makes the encryption effect better. Therefore, the proposed chaotic system can be used as a pseudo-random sequence generator to provide key sequences for digital encryption systems. Thus, the chaotic system is discretized and implemented by Digital Signal Processing (DSP) technology. The National Institute of Standards and Technology (NIST) test and Approximate Entropy analysis of the proposed chaotic system are conducted in this paper.

[1]  Fuad E. Alsaadi,et al.  A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control , 2018, Chinese Physics B.

[2]  Elaine B. Barker,et al.  A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications , 2000 .

[3]  Kehui Sun,et al.  Complexity Analysis and DSP Implementation of the Fractional-Order Lorenz Hyperchaotic System , 2015, Entropy.

[4]  Mauro Forti,et al.  New Conditions for Global Asymptotic Stability of Memristor Neural Networks , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[5]  Guanrong Chen,et al.  A chaos-based image encryption algorithm with variable control parameters , 2009 .

[6]  Daniel D. Wheeler,et al.  Supercomputer Investigations of a Chaotic Encryption Algorithm , 1991, Cryptologia.

[7]  Fang Yuan,et al.  Complex Dynamics in a Memcapacitor-Based Circuit , 2019, Entropy.

[8]  Said Hamdioui,et al.  A Mapping Methodology of Boolean Logic Circuits on Memristor Crossbar , 2018, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[9]  Eby G. Friedman,et al.  Memristor-Based Circuit Design for Multilayer Neural Networks , 2018, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  Leon O. Chua,et al.  Local Activity is the Origin of Complexity , 2005, Int. J. Bifurc. Chaos.

[11]  Jesus M. Munoz-Pacheco,et al.  Chaos generation in fractional-order switched systems and its digital implementation , 2017 .

[12]  Pramod K. Varshney,et al.  A Memristor-Based Optimization Framework for Artificial Intelligence Applications , 2018, IEEE Circuits and Systems Magazine.

[13]  Wang Guangyi,et al.  Meminductive Wein-bridge chaotic oscillator , 2017 .

[14]  Nithin Nagaraj,et al.  Increasing average period lengths by switching of robust chaos maps in finite precision , 2008, 0811.1823.

[15]  Yuxia Li,et al.  Dynamic Analysis of a Bistable Bi-Local Active Memristor and Its Associated Oscillator System , 2018, Int. J. Bifurc. Chaos.

[16]  Zhijun Li,et al.  A simple inductor-free memristive circuit with three line equilibria , 2018, Nonlinear Dynamics.

[17]  Naixue Xiong,et al.  Analysis and Design of Digital Chaotic Systems With Desirable Performance via Feedback Control , 2015, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[18]  Yasser Shekofteh,et al.  A New Chaotic System with a Self-Excited Attractor: Entropy Measurement, Signal Encryption, and Parameter Estimation , 2018, Entropy.

[19]  Huaqiang Wu,et al.  An artificial nociceptor based on a diffusive memristor , 2018, Nature Communications.

[20]  Sen Zhang,et al.  Generating one to four-wing hidden attractors in a novel 4D no-equilibrium chaotic system with extreme multistability. , 2018, Chaos.

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

[22]  Leon O. Chua,et al.  Circuit Elements With Memory: Memristors, Memcapacitors, and Meminductors , 2009, Proceedings of the IEEE.

[23]  X. Mou,et al.  Improving security of a chaotic encryption approach , 2001, Physics Letters A.

[24]  Qun Ding,et al.  A Novel Image Encryption Scheme Based on Self-Synchronous Chaotic Stream Cipher and Wavelet Transform , 2018, Entropy.

[25]  Clare D. McGillem,et al.  A chaotic direct-sequence spread-spectrum communication system , 1994, IEEE Trans. Commun..

[26]  Sunil R. Das,et al.  Memristor-Based High-Speed Memory Cell With Stable Successive Read Operation , 2018, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

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

[28]  Zhisen Wang,et al.  Dynamics analysis of Wien-bridge hyperchaotic memristive circuit system , 2018 .

[29]  Leon O. Chua,et al.  Everything You Wish to Know About Memristors but Are Afraid to Ask , 2015, Handbook of Memristor Networks.

[30]  Mei Guo,et al.  Dynamics of a physical SBT memristor-based Wien-bridge circuit , 2018 .

[31]  Hangbing Lv,et al.  An Artificial Neuron Based on a Threshold Switching Memristor , 2018, IEEE Electron Device Letters.

[32]  J. Cernák.  Digital generators of chaos , 1996 .

[33]  Guangyi Wang,et al.  A Locally Active Memristor and Its Application in a Chaotic Circuit , 2018, IEEE Transactions on Circuits and Systems II: Express Briefs.

[34]  Yu Zhang,et al.  Coexisting multiple attractors and riddled basins of a memristive system. , 2018, Chaos.

[35]  Qiang Lai,et al.  A New Chaotic System with Multiple Attractors: Dynamic Analysis, Circuit Realization and S-Box Design , 2017, Entropy.

[36]  Leon O. Chua.  Resistance switching memories are memristors , 2011 .

[37]  L.O. Chua,et al.  Memristive devices and systems , 1976, Proceedings of the IEEE.

[38]  Kaijun Wu,et al.  Chaotic Adaptive Synchronization Control and Application in Chaotic Secure Communication for Industrial Internet of Things , 2018, IEEE Access.

[39]  Yan Li,et al.  Design and circuit implementation of a five‐dimensional hyperchaotic system with linear parameter , 2018, International journal of circuit theory and applications.

[40]  Zhigang Zeng,et al.  A Novel Design for Memristor-Based Multiplexer Via NOT-Material Implication , 2018, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[41]  Lih-Yuan Deng,et al.  Period Extension and Randomness Enhancement Using High-Throughput Reseeding-Mixing PRNG , 2012, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[42]  Leon O. Chua,et al.  Three Fingerprints of Memristor , 2013, IEEE Transactions on Circuits and Systems I: Regular Papers.

[43]  Martins Ezuma,et al.  A New Chaotic Oscillator—Properties, Analog Implementation, and Secure Communication Application , 2019, IEEE Access.

[44]  Yuxia Li,et al.  A Color Image Encryption Algorithm Based on a Fractional-Order Hyperchaotic System , 2014, Entropy.

[45]  Sen Zhang,et al.  Generating hidden extreme multistability in memristive chaotic oscillator via micro‐perturbation , 2018, Electronics Letters.

[46]  Zhen Wang,et al.  Nonlinear dynamics and chaos in a simplified memristor-based fractional-order neural network with discontinuous memductance function , 2018, Nonlinear Dynamics.

[47]  Ziqi Zhu,et al.  A method of improving the properties of digital chaotic system , 2008 .

[48]  Chunbiao Li,et al.  A Memristive Chaotic Oscillator With Increasing Amplitude and Frequency , 2018, IEEE Access.

[49]  Zhen Wang,et al.  Unstable Limit Cycles and Singular Attractors in a Two-Dimensional Memristor-Based Dynamic System , 2019, Entropy.

[50]  Fang Yuan,et al.  The amplitude, frequency and parameter space boosting in a memristor–meminductor-based circuit , 2019, Nonlinear Dynamics.

[51]  J. Kengne,et al.  Dynamical analysis and multistability in autonomous hyperchaotic oscillator with experimental verification , 2018 .

[52]  Sang Tao,et al.  Perturbance-based algorithm to expand cycle length of chaotic key stream , 1998 .

[53]  Jacques Kengne,et al.  Dynamic analysis and multistability of a novel four-wing chaotic system with smooth piecewise quadratic nonlinearity , 2018, Chaos, Solitons & Fractals.