Coexistence of hidden chaotic attractors in a novel no-equilibrium system

Hidden attractors have received considerable interest in physics, mechanics and other dynamical areas recently. This paper introduces a novel autonomous system with hidden attractor. In particular, there exists no-equilibrium point in this system. Although the new system is simple with six terms, it exhibits complex behavior such as chaos and multistability. In addition, the offset boosting of a variable is achieved by adding a single controlled constant. Dynamical properties of the no-equilibrium system have been discovered by using nonlinear dynamical tools as well as an electronic implementation.

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

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

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

[4]  Tomasz Kapitaniak,et al.  Rare and hidden attractors in Van der Pol-Duffing oscillators , 2015 .

[5]  Runtong Chu,et al.  Selection of multi-scroll attractors in Jerk circuits and their verification using Pspice , 2014 .

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

[7]  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.

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

[9]  Julien Clinton Sprott,et al.  Recent new examples of hidden attractors , 2015 .

[10]  Sergey P. Kuznetsov,et al.  Co-existing hidden attractors in a radio-physical oscillator system , 2015 .

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

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

[13]  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 .

[14]  Zhouchao Wei,et al.  Dynamics and delayed feedback control for a 3D jerk system with hidden attractor , 2015 .

[15]  Julien Clinton Sprott,et al.  Finding coexisting attractors using amplitude control , 2014 .

[16]  G. Leonov,et al.  Hidden attractors in dynamical systems , 2016 .

[17]  Lin Wang,et al.  3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system , 2009 .

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

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

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

[21]  Weiwei Liu,et al.  Designing S-boxes based on 3-D four-wing autonomous chaotic system , 2015 .

[22]  R. Leipnik,et al.  Double strange attractors in rigid body motion with linear feedback control , 1981 .

[23]  Shandelle M Henson,et al.  Multiple mixed-type attractors in a competition model , 2007, Journal of biological dynamics.

[24]  Luigi Fortuna,et al.  Design of Time-Delay Chaotic Electronic Circuits , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[25]  J. Sprott,et al.  Some simple chaotic flows. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

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

[27]  K. Kyamakya,et al.  On the analysis of semiconductor diode-based chaotic and hyperchaotic generators—a case study , 2014 .

[28]  Awadhesh Prasad,et al.  Perpetual points and hidden attractors in dynamical systems , 2015 .

[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.  Constructing Chaotic Systems with Total Amplitude Control , 2015, Int. J. Bifurc. Chaos.

[31]  Przemyslaw Perlikowski,et al.  Multistability and Rare attractors in van der Pol-Duffing oscillator , 2011, Int. J. Bifurc. Chaos.

[32]  Nikolay V. Kuznetsov,et al.  Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuits , 2011 .

[33]  Luigi Fortuna,et al.  A Simple Chaotic Flow with a Continuously Adjustable Attractor Dimension , 2015, Int. J. Bifurc. Chaos.

[34]  Mohammad Ghasem Mahjani,et al.  Multiple attractors in Koper–Gaspard model of electrochemical periodic and chaotic oscillations , 2010 .

[35]  J. Llibre.  Centers: their integrability and relations with the divergence , 2016 .

[36]  Erik Mosekilde,et al.  Multistability and hidden attractors in a multilevel DC/DC converter , 2015, Math. Comput. Simul..

[37]  Luigi Fortuna,et al.  A chaotic circuit based on Hewlett-Packard memristor. , 2012, Chaos.

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

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

[40]  Ma Jun,et al.  Realization of synchronization between hyperchaotic systems by using a scheme of intermittent linear coupling , 2013 .

[41]  Tomasz Kapitaniak,et al.  Multistability: Uncovering hidden attractors , 2015, The European Physical Journal Special Topics.

[42]  Nikolay V. Kuznetsov,et al.  Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor , 2014 .

[43]  Guanrong Chen,et al.  Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications , 2006 .

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

[45]  Masoller.  Coexistence of attractors in a laser diode with optical feedback from a large external cavity. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[46]  Tariq Shah,et al.  An efficient technique for the construction of substitution box with chaotic partial differential equation , 2013, Nonlinear Dynamics.

[47]  Zhigang Zeng,et al.  Multistability of Neural Networks With Time-Varying Delays and Concave-Convex Characteristics , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[48]  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 .

[49]  Awadhesh Prasad,et al.  Existence of Perpetual Points in Nonlinear Dynamical Systems and Its Applications , 2014, Int. J. Bifurc. Chaos.

[50]  Qigui Yang,et al.  Dynamical analysis of a new autonomous 3-D chaotic system only with stable equilibria , 2011 .

[51]  Ioannis M. Kyprianidis,et al.  A chaotic path planning generator for autonomous mobile robots , 2012, Robotics Auton. Syst..

[52]  Bishnu Charan Sarkar,et al.  Design and analysis of a first order time-delayed chaotic system , 2012 .

[53]  Ranjit Kumar Upadhyay,et al.  Multiple attractors and crisis route to chaos in a model food-chain , 2003 .

[54]  Chai Wah Wu,et al.  Chua's oscillator: A compendium of chaotic phenomena , 1994 .

[55]  Zhigang Zeng,et al.  Multistability of Recurrent Neural Networks With Time-varying Delays and the Piecewise Linear Activation Function , 2010, IEEE Transactions on Neural Networks.

[56]  Zhouchao Wei,et al.  Dynamical behaviors of a chaotic system with no equilibria , 2011 .