Uncertain destination dynamics of a novel memristive 4D autonomous system

Abstract This paper studies the dynamics of a novel memristive 4D autonomous system obtained by replacing the memristive diode bridge in the original circuit of [Chaos, Solitons and Fractals 91 180–197 (2016)] with a flux control memristor. The new memristor oscillator is described by a continuous time four-dimensional autonomous system with a line of equilibria. The analysis is carried out in terms of its parameters by using bifurcation diagrams, phase space trajectory plots, Poincare sections, bifurcation like sequences, and graphs of Lyapunov exponents. The system is shown to experience the unusual phenomenon of extreme multistability characterized by the possibility of an infinite number of attractors for the same parameters setting. Period doubling and symmetry restoring crisis scenarios are reported. To the best of the authors’ knowledge, the results of this work represent the first report on the phenomenon of extreme multistability in a jerk system and thus deserve dissemination.

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

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

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

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

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

[6]  Bocheng Bao,et al.  Extreme multistability in a memristive circuit , 2016 .

[7]  Julien Clinton Sprott,et al.  Transformation of 4-D dynamical systems to hyperjerk form , 2013 .

[8]  Sundarapandian Vaidyanathan,et al.  A Chaotic System with Different Families of Hidden Attractors , 2016, Int. J. Bifurc. Chaos.

[9]  Fernando Corinto,et al.  Memristor Circuits: Bifurcations without Parameters , 2017, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  K Showalter,et al.  Uncertain destination dynamics. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  Buncha Munmuangsaen,et al.  Elementary chaotic snap flows , 2011 .

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

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

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

[15]  Julien Clinton Sprott,et al.  Chaotic hyperjerk systems , 2006 .

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

[17]  S K Dana,et al.  How to obtain extreme multistability in coupled dynamical systems. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[19]  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 .

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

[21]  Qingdu Li,et al.  Hyperchaos in a 4D memristive circuit with infinitely many stable equilibria , 2015 .

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

[23]  Kenneth Showalter,et al.  Uncertain dynamics in nonlinear chemical reactions , 2003 .

[24]  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..

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

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

[27]  Kenneth Showalter,et al.  Extreme multistability in a chemical model system. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Viet-Thanh Pham,et al.  Multiscroll Chaotic Sea Obtained from a Simple 3D System Without Equilibrium , 2016, Int. J. Bifurc. Chaos.

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

[30]  Stefan J. Linz,et al.  On hyperjerky systems , 2008 .

[31]  Fernando Corinto,et al.  Memristor Circuits: Flux—Charge Analysis Method , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.