Antimonotonicity, chaos and multiple coexisting attractors in a simple hybrid diode-based jerk circuit

Abstract This paper focuses on the dynamics of a modified jerk circuit obtained via replacing the diode bridge memristor in the original jerk circuit introduced in [24] with a first-order hybrid diode circuit. Both memristive diode bridge and first order hybrid diode are frequency dependent component even though the later device doesn't has a pinched hysteresis loop. The analysis is carried out in terms of bifurcation diagrams, graph of Lyapunov exponents, phase portraits, Poincare section, time series and frequency spectra. The results indicate that, the new circuit exhibits rich dynamic behaviors including multiple coexisting self-excited attractors (e.g. coexistence of two, four or six disconnected periodic and chaotic attractors) and antimonotonicity (i.e. concurrent creation and annihilation of periodic orbits) compared to the original memrisitve jerk circuit. Basins of attraction of various coexisting attractors display extremely complex structures thus justifying jumps between coexisting attractors in experiment. Both PSpice simulations and laboratory experimental measurements are carried out to support the theoretical analyses.

[1]  Takashi Matsumoto,et al.  A chaotic attractor from Chua's circuit , 1984 .

[2]  Mo Chen,et al.  Self-Excited and Hidden Attractors Found Simultaneously in a Modified Chua's Circuit , 2015, Int. J. Bifurc. Chaos.

[3]  Jacques Kengne,et al.  Dynamical analysis of a simple autonomous jerk system with multiple attractors , 2016 .

[4]  A. Nayfeh,et al.  Applied nonlinear dynamics : analytical, computational, and experimental methods , 1995 .

[5]  Julien Clinton Sprott,et al.  Simple chaotic systems and circuits , 2000 .

[6]  I. Raja Mohamed,et al.  Duffing–van der Pol oscillator type dynamics in Murali–Lakshmanan–Chua (MLC) circuit , 2016 .

[7]  Bharat Bhushan Sharma,et al.  Nonlinear unknown input sliding mode observer based chaotic system synchronization and message recovery scheme with uncertainty , 2017 .

[8]  J. Yorke,et al.  Antimonotonicity: inevitable reversals of period-doubling cascades , 1992 .

[9]  Grebogi,et al.  Geometric mechanism for antimonotonicity in scalar maps with two critical points. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Leon O. Chua,et al.  EXPERIMENTAL OBSERVATION OF ANTIMONOTONICITY IN CHUA'S CIRCUIT , 1993 .

[11]  Sundarapandian Vaidyanathan,et al.  A new four-scroll chaotic attractor and its engineering applications , 2016 .

[12]  Nisha Gupta,et al.  Realization of Chaotic Circuits Using Lambda Diode , 2017, J. Circuits Syst. Comput..

[13]  Mo Chen,et al.  A Memristive Diode Bridge-Based Canonical Chua's Circuit , 2014, Entropy.

[14]  Jacques Kengne,et al.  Nonlinear behavior of a novel chaotic jerk system: antimonotonicity, crises, and multiple coexisting attractors , 2018 .

[15]  Parlitz,et al.  Period-doubling cascades and devil's staircases of the driven van der Pol oscillator. , 1987, Physical review. A, General physics.

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

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

[18]  Guanrong Chen,et al.  Diagnosing multistability by offset boosting , 2017 .

[19]  Leandro M Alonso,et al.  Nonlinear resonances and multi-stability in simple neural circuits. , 2016, Chaos.

[20]  A. G. Rigas,et al.  Time series analysis in chaotic diode resonator circuit , 2006 .

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

[22]  Viet-Thanh Pham,et al.  A Chaotic System with Two Stable Equilibrium Points: Dynamics, Circuit Realization and Communication Application , 2017, Int. J. Bifurc. Chaos.

[23]  Akif Akgul,et al.  A simple chaotic circuit with a hyperbolic sine function and its use in a sound encryption scheme , 2017 .

[24]  Nikolay V. Kuznetsov,et al.  Hidden attractor in the Rabinovich system, Chua circuits and PLL , 2016 .

[25]  Jacques Kengne,et al.  Dynamic analysis and electronic circuit implementation of a novel 3D autonomous system without linear terms , 2017, Commun. Nonlinear Sci. Numer. Simul..

[26]  Jacques Kengne,et al.  Coexistence of Chaos with Hyperchaos, Period-3 Doubling Bifurcation, and Transient Chaos in the Hyperchaotic Oscillator with Gyrators , 2015, Int. J. Bifurc. Chaos.

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

[28]  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 .

[29]  Zhong Liu,et al.  Generalized Memristor Consisting of Diode Bridge with First Order Parallel RC Filter , 2014, Int. J. Bifurc. Chaos.

[30]  Gregor Strobbe,et al.  EEG Derived Brain Activity Reflects Treatment Response from Vagus Nerve Stimulation in Patients with Epilepsy , 2017, Int. J. Neural Syst..

[31]  Tassos Bountis,et al.  Remerging Feigenbaum trees in dynamical systems , 1984 .

[32]  Michael Peter Kennedy,et al.  Nonlinear analysis of the Colpitts oscillator and applications to design , 1999 .

[33]  Paul Woafo,et al.  Hartley’s oscillator: The simplest chaotic two-component circuit , 2012 .

[34]  P. Woafo,et al.  Dynamics of coupled simplest chaotic two-component electronic circuits and its potential application to random bit generation. , 2013, Chaos.

[36]  Fuhong Min,et al.  Multistability analysis, circuit implementations and application in image encryption of a novel memristive chaotic circuit , 2017, Nonlinear Dynamics.

[37]  Julien Clinton Sprott,et al.  A New Chaotic Jerk Circuit , 2011, IEEE Transactions on Circuits and Systems II: Express Briefs.

[38]  Jacques Kengne,et al.  Coexistence of multiple attractors and crisis route to chaos in autonomous third order Duffing-Holmes type chaotic oscillators , 2016, Commun. Nonlinear Sci. Numer. Simul..

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

[40]  Luigi Fortuna,et al.  Chaotic pulse position modulation to improve the efficiency of sonar sensors , 2003, IEEE Trans. Instrum. Meas..

[41]  Ioannis M. Kyprianidis,et al.  Image encryption process based on chaotic synchronization phenomena , 2013, Signal Process..

[42]  Daniel J. Gauthier,et al.  Controlling chaos in a fast diode resonator using extended time-delay autosynchronization: Experimental observations and theoretical analysis. , 1997, Chaos.

[43]  Robert C. Hilborn,et al.  Chaos And Nonlinear Dynamics: An Introduction for Scientists and Engineers , 1994 .

[44]  Viet-Thanh Pham,et al.  Generating a Chaotic System with One Stable Equilibrium , 2017, Int. J. Bifurc. Chaos.

[45]  A. Wolf,et al.  Determining Lyapunov exponents from a time series , 1985 .

[46]  Y. Uyaroglu,et al.  A new chaotic attractor from general Lorenz system family and its electronic experimental implementation , 2010 .