Multistability in Chua's circuit with two stable node-foci.

Only using one-stage op-amp based negative impedance converter realization, a simplified Chua's diode with positive outer segment slope is introduced, based on which an improved Chua's circuit realization with more simpler circuit structure is designed. The improved Chua's circuit has identical mathematical model but completely different nonlinearity to the classical Chua's circuit, from which multiple attractors including coexisting point attractors, limit cycle, double-scroll chaotic attractor, or coexisting chaotic spiral attractors are numerically simulated and experimentally captured. Furthermore, with dimensionless Chua's equations, the dynamical properties of the Chua's system are studied including equilibrium and stability, phase portrait, bifurcation diagram, Lyapunov exponent spectrum, and attraction basin. The results indicate that the system has two symmetric stable nonzero node-foci in global adjusting parameter regions and exhibits the unusual and striking dynamical behavior of multiple attractors with multistability.

[1]  Awadhesh Prasad,et al.  Complicated basins and the phenomenon of amplitude death in coupled hidden attractors , 2014 .

[2]  Julien Clinton Sprott,et al.  Simple Chaotic flows with One Stable equilibrium , 2013, Int. J. Bifurc. Chaos.

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

[4]  Nikolay V. Kuznetsov,et al.  On differences and similarities in the analysis of Lorenz, Chen, and Lu systems , 2014, Appl. Math. Comput..

[5]  Y. Lai,et al.  Transient chaos in optical metamaterials. , 2011, Chaos.

[6]  Qigui Yang,et al.  A Chaotic System with One saddle and Two Stable Node-Foci , 2008, Int. J. Bifurc. Chaos.

[7]  Julien Clinton Sprott,et al.  A chaotic system with a single unstable node , 2015 .

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

[9]  Nikolay V. Kuznetsov,et al.  Analytical-Numerical Localization of Hidden Attractor in Electrical Chua’s Circuit , 2013 .

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

[11]  Ahmed S. Elwakil,et al.  Creation of a complex butterfly attractor using a novel Lorenz-Type system , 2002 .

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

[13]  Julien Clinton Sprott,et al.  Simple chaotic flows with a line equilibrium , 2013 .

[14]  Bocheng Bao,et al.  Hidden attractors in a practical Chua's circuit based on a modified Chua's diode , 2016 .

[15]  M. Lakshmanan,et al.  Nonsmooth bifurcations, Transient Hyperchaos and hyperchaotic beats in a Memristive Murali-Lakshmanan-Chua Circuit , 2013, Int. J. Bifurc. Chaos.

[16]  Xinghuo Yu,et al.  Design and Implementation of Grid Multiwing Hyperchaotic Lorenz System Family via Switching Control and Constructing Super-Heteroclinic Loops , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[17]  U. Feudel,et al.  Control of multistability , 2014 .

[18]  Viet-Thanh Pham,et al.  Synchronization and circuit design of a chaotic system with coexisting hidden attractors , 2015 .

[19]  Ahmed S. Elwakil,et al.  Improved implementation of Chua's chaotic oscillator using current feedback op amp , 2000 .

[20]  P. Arena,et al.  Chua's circuit can be generated by CNN cells , 1995 .

[21]  Awadhesh Prasad,et al.  Controlling Dynamics of Hidden Attractors , 2015, Int. J. Bifurc. Chaos.

[22]  Julien Clinton Sprott,et al.  A New Piecewise Linear Hyperchaotic Circuit , 2014, IEEE Transactions on Circuits and Systems II: Express Briefs.

[23]  Bocheng Bao,et al.  Finding hidden attractors in improved memristor-based Chua''s circuit , 2015 .

[24]  Saverio Morfu,et al.  On the use of multistability for image processing , 2007 .

[25]  Nikolay V. Kuznetsov,et al.  Hidden attractor in smooth Chua systems , 2012 .

[26]  R. E. Amritkar,et al.  Experimental observation of extreme multistability in an electronic system of two coupled Rössler oscillators. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Nikolay V. Kuznetsov,et al.  Hidden attractors in Dynamical Systems. From Hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits , 2013, Int. J. Bifurc. Chaos.

[28]  Ludovico Minati,et al.  Experimental dynamical characterization of five autonomous chaotic oscillators with tunable series resistance. , 2014, Chaos.

[29]  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.

[30]  Julien Clinton Sprott,et al.  Coexisting Hidden Attractors in a 4-D Simplified Lorenz System , 2014, Int. J. Bifurc. Chaos.

[31]  Roberto Tonelli,et al.  Experimental Definition of the Basin of attraction for Chua's Circuit , 2000, Int. J. Bifurc. Chaos.

[32]  S. K. Dana,et al.  Extreme multistability: Attractor manipulation and robustness. , 2015, Chaos.

[33]  Nikolay V. Kuznetsov,et al.  Hidden attractor and homoclinic orbit in Lorenz-like system describing convective fluid motion in rotating cavity , 2015, Commun. Nonlinear Sci. Numer. Simul..

[34]  Guanrong Chen,et al.  A general multiscroll Lorenz system family and its realization via digital signal processors. , 2006, Chaos.

[35]  Makoto Itoh.  Synthesis of Electronic Circuits for Simulating nonlinear Dynamics , 2001, Int. J. Bifurc. Chaos.

[36]  Bocheng Bao,et al.  Dynamics of self-excited attractors and hidden attractors in generalized memristor-based Chua’s circuit , 2015 .

[37]  Qingdu Li,et al.  On hidden twin attractors and bifurcation in the Chua’s circuit , 2014 .

[38]  Leon O. Chua,et al.  Double scroll via a two-transistor circuit , 1986 .

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

[40]  T. N. Mokaev,et al.  Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion Homoclinic orbits, and self-excited and hidden attractors , 2015 .

[41]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

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

[43]  Michael Peter Kennedy,et al.  Robust OP Amp Realization of Chua's Circuit , 1992 .

[44]  Julien Clinton Sprott,et al.  Coexistence of Point, periodic and Strange attractors , 2013, Int. J. Bifurc. Chaos.

[45]  Julien Clinton Sprott,et al.  Multistability in the Lorenz System: A Broken Butterfly , 2014, Int. J. Bifurc. Chaos.

[46]  Julien Clinton Sprott,et al.  Elementary quadratic chaotic flows with no equilibria , 2013 .