Complex dynamics of a modified four order Wien-bridge oscillator model and FPGA implementation

This paper presents a novel fourth-order autonomous flux controlled memristive Wien-bridge system. Standard nonlinear diagnostic tools such as bifurcation diagram, graphs of largest Lyapunov exponent, Lyapunov stability diagram, phase space trajectory and isospike diagram are used to characterize dynamics of the system. Results show that the system presents hidden attractors with infinite equilibrium points known as line equilibrium for a suitable set of its parameters. The system also exhibits striking phenomenon of extreme multistability. Through isospike and Lyapunov stability diagram, spiral bifurcation leading to a center hub point is observed in a Wien-bridge circuit for the first time and the Field Programmable Gate Array -based implementation is performed to confirm its feasibility.

[1]  Bocheng Bao,et al.  Hidden extreme multistability in memristive hyperchaotic system , 2017 .

[2]  Jacques Kengne,et al.  Dynamical analysis and electronic circuit realization of an equilibrium free 3D chaotic system with a large number of coexisting attractors , 2017 .

[3]  Vaithianathan Venkatasubramanian,et al.  Coexistence of four different attractors in a fundamental power system model , 1999 .

[4]  Mohammed F. Tolba,et al.  Fractional X-shape controllable multi-scroll attractor with parameter effect and FPGA automatic design tool software , 2019, Chaos, Solitons & Fractals.

[5]  Binoy Krishna Roy,et al.  Hidden attractors in a new complex generalised Lorenz hyperchaotic system, its synchronisation using adaptive contraction theory, circuit validation and application , 2018 .

[6]  Viet-Thanh Pham,et al.  A new 4D chaotic system with hidden attractor and its engineering applications: Analog circuit design and field programmable gate array implementation , 2018 .

[7]  Yoshihiko Nakamura,et al.  The chaotic mobile robot , 2001, IEEE Trans. Robotics Autom..

[8]  Leon O. Chua,et al.  MEMRISTOR CELLULAR AUTOMATA AND MEMRISTOR DISCRETE-TIME CELLULAR NEURAL NETWORKS , 2009 .

[9]  Bocheng Bao,et al.  Multiple attractors in a non-ideal active voltage-controlled memristor based Chua's circuit , 2016 .

[10]  Jacques Kengne,et al.  Coexistence of Multiple Attractors and Crisis Route to Chaos in a Novel Chaotic Jerk Circuit , 2016, Int. J. Bifurc. Chaos.

[11]  Ahmad Taher Azar,et al.  Multistability Analysis and Function Projective Synchronization in Relay Coupled Oscillators , 2018, Complex..

[12]  E. Tlelo-Cuautle,et al.  Generating a 50-scroll chaotic attractor at 66 MHz by using FPGAs , 2016 .

[13]  Ahmed M. Soliman,et al.  Generalized fractional logistic map encryption system based on FPGA , 2017 .

[14]  Karthikeyan Rajagopal,et al.  FPGA implementation of novel fractional-order chaotic systems with two equilibriums and no equilibrium and its adaptive sliding mode synchronization , 2017 .

[15]  Jacques Kengne,et al.  Antimonotonicity, chaos and multiple attractors in a novel autonomous memristor-based jerk circuit , 2017 .

[16]  Jacques Kengne,et al.  On the Dynamics of Chua’s oscillator with a smooth cubic nonlinearity: occurrence of multiple attractors , 2017 .

[17]  Mattia Frasca,et al.  A true random bit generator based on a memristive chaotic circuit: Analysis, design and FPGA implementation , 2019, Chaos, Solitons & Fractals.

[18]  Xu Jianping,et al.  Mapping equivalent approach to analysis and realization of memristor-based dynamical circuit , 2014 .

[19]  Yi Wang,et al.  A Phase-Locking Analysis of Neuronal Firing Rhythms with Transcranial Magneto-Acoustical Stimulation Based on the Hodgkin-Huxley Neuron Model , 2017, Front. Comput. Neurosci..

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

[21]  P. Glendinning,et al.  Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Karthikeyan Rajagopal,et al.  Fractional Order Memristor No Equilibrium Chaotic System with Its Adaptive Sliding Mode Synchronization and Genetically Optimized Fractional Order PID Synchronization , 2017, Complex..

[23]  J. G. Freire,et al.  Stern-Brocot trees in the periodicity of mixed-mode oscillations. , 2011, Physical chemistry chemical physics : PCCP.

[24]  G. Leonov,et al.  Localization of hidden Chuaʼs attractors , 2011 .

[25]  A. Tamasevicius,et al.  Modified Wien-bridge oscillator for chaos , 1995 .

[26]  Jacques Kengne,et al.  Uncertain destination dynamics of a novel memristive 4D autonomous system , 2018 .

[27]  G. Leonov,et al.  Hidden oscillations in dynamical systems , 2011 .

[28]  Cecilia Cabeza,et al.  Periodicity hubs and wide spirals in a two-component autonomous electronic circuit , 2013 .

[29]  Bocheng Bao,et al.  Parameter-Independent Dynamical Behaviors in Memristor-Based Wien-Bridge Oscillator , 2017 .

[30]  Jacques Kengne,et al.  Antimonotonicity, chaos and multiple coexisting attractors in a simple hybrid diode-based jerk circuit , 2017 .

[31]  Huagan Wu,et al.  Complex transient dynamics in periodically forced memristive Chua’s circuit , 2015 .

[32]  Massimiliano Di Ventra,et al.  Memristive model of amoeba learning. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Kyungmin Kim,et al.  Memristor Applications for Programmable Analog ICs , 2011, IEEE Transactions on Nanotechnology.

[34]  Ahmed S. Elwakil,et al.  Two Modified for Chaos Negative Impedance Converter Op Amp Oscillators with Symmetrical and Antisymmetrical Nonlinearities , 1998 .

[35]  Nikolay V. Kuznetsov,et al.  Hidden Attractor in Chua's Circuits , 2011, ICINCO.

[36]  Huagan Wu,et al.  A Simple Third-Order Memristive Band Pass Filter Chaotic Circuit , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[37]  Jacques Kengne,et al.  Coexistence of multiple attractors and crisis route to chaos in a novel memristive diode bidge-based Jerk circuit , 2016 .

[38]  Ioannis M. Kyprianidis,et al.  Antimonotonicity and Chaotic Dynamics in a Fourth-Order Autonomous nonlinear Electric Circuit , 2000, Int. J. Bifurc. Chaos.

[39]  Nikolay V. Kuznetsov,et al.  Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems , 2011 .

[40]  Z. Njitacke Tabekoueng,et al.  Periodicity, chaos, and multiple attractors in a memristor-based Shinriki's circuit. , 2015, Chaos.

[41]  Andrey Shilnikov,et al.  Kneadings, Symbolic Dynamics and Painting Lorenz Chaos , 2012, Int. J. Bifurc. Chaos.

[42]  Mo Chen,et al.  Coexisting Behaviors of Asymmetric Attractors in Hyperbolic-Type Memristor based Hopfield Neural Network , 2017, Front. Comput. Neurosci..

[43]  Huagan Wu,et al.  Numerical analyses and experimental validations of coexisting multiple attractors in Hopfield neural network , 2017 .

[44]  Nikolay V. Kuznetsov,et al.  Hidden oscillations in nonlinear control systems , 2011 .

[45]  Chunhua Wang,et al.  A new simple chaotic circuit based on memristor and meminductor , 2016, The European Physical Journal Plus.

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

[47]  Mauro Forti,et al.  Convergence and Multistability of Nonsymmetric Cellular Neural Networks With Memristors , 2017, IEEE Transactions on Cybernetics.

[48]  Ömer Morgül.  Wien bridge based RC chaos generator , 1995 .

[49]  Huagan Wu,et al.  Symmetric periodic bursting behavior and bifurcation mechanism in a third-order memristive diode bridge-based oscillator , 2018 .

[50]  Nikolay V. Kuznetsov,et al.  Analytical-numerical method for attractor localization of generalized Chua's system , 2010, PSYCO.

[51]  Kyandoghere Kyamakya,et al.  Regular oscillations, chaos, and multistability in a system of two coupled van der Pol oscillators: numerical and experimental studies , 2014 .

[52]  M. Yao,et al.  Study of hidden attractors, multiple limit cycles from Hopf bifurcation and boundedness of motion in the generalized hyperchaotic Rabinovich system , 2015 .

[53]  Sallee Klein,et al.  Memristive Adaptive Filters , 2010 .

[54]  Xiao-Song Yang,et al.  Hyperchaos and bifurcation in a new class of four-dimensional Hopfield neural networks , 2006, Neurocomputing.

[55]  Dongsheng Yu,et al.  Hyperchaos in a memristor-Based Modified Canonical Chua's Circuit , 2012, Int. J. Bifurc. Chaos.

[56]  J. G. Freire,et al.  Stern-Brocot trees in cascades of mixed-mode oscillations and canards in the extended Bonhoeffer-van der Pol and the FitzHugh-Nagumo models of excitable systems , 2011 .

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

[58]  Nikolay V. Kuznetsov,et al.  Analytical-numerical methods for investigation of hidden oscillations in nonlinear control systems , 2011 .

[59]  Ioannis M. Kyprianidis,et al.  Chaotic behaviour of a fourth-order autonomous electric circuit , 2003 .

[60]  X. Liao,et al.  Cryptanalysis and improvement on a block cryptosystem based on iteration a chaotic map , 2007 .

[61]  Bocheng Bao,et al.  Numerical and experimental confirmations of quasi-periodic behavior and chaotic bursting in third-order autonomous memristive oscillator , 2018 .

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