Simulation and experimental implementation of a line–equilibrium system without linear term

Abstract Simulation and experimental implementation have been applied to investigate a new chaotic flow, which has a line of equilibria. The new chaotic flow is based on a general model. The system has five non-linear terms and only one parameter, therefore it is considered as a system without linear terms. By changing the only parameter, we observe system’s dynamics. The system is realized in a circuit, which is measured for comparison of simulations and experiments.

[1]  Julien Clinton Sprott,et al.  Bistability in a hyperchaotic system with a line equilibrium , 2014 .

[2]  Jesus M. Munoz-Pacheco,et al.  Chaos generation in fractional-order switched systems and its digital implementation , 2017 .

[3]  Luigi Fortuna,et al.  A Concise Guide to Chaotic Electronic Circuits , 2014 .

[4]  L. Minati Experimental Implementation of Networked Chaotic Oscillators Based on Cross-Coupled Inverter Rings in a CMOS Integrated Circuit , 2015, J. Circuits Syst. Comput..

[5]  E. Campos-Cantón,et al.  Strange attractors generated by a fractional order switching system and its topological horseshoe , 2016 .

[6]  Julien Clinton Sprott,et al.  Simple Chaotic Hyperjerk System , 2016, Int. J. Bifurc. Chaos.

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

[8]  Sen Zhang,et al.  Chaos in a novel fractional order system without a linear term , 2018, International Journal of Non-Linear Mechanics.

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

[10]  Buncha Munmuangsaen,et al.  A new five-term simple chaotic attractor , 2009 .

[11]  L. Minati Remote synchronization of amplitudes across an experimental ring of non-linear oscillators. , 2015, Chaos.

[12]  Nikolay V. Kuznetsov,et al.  Matlab Code for Lyapunov Exponents of Fractional-Order Systems , 2018, Int. J. Bifurc. Chaos.

[13]  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.

[14]  Qigui Yang,et al.  A new Lorenz-type hyperchaotic system with a curve of equilibria , 2015, Math. Comput. Simul..

[15]  Julien Clinton Sprott,et al.  Simple chaotic 3D flows with surfaces of equilibria , 2016 .

[16]  Guanrong Chen,et al.  Constructing a chaotic system with any number of equilibria , 2012, 1201.5751.

[17]  Luigi Fortuna,et al.  Emulating complex business cycles by using an electronic analogue , 2012 .

[18]  José-Cruz Nuñez Pérez,et al.  FPGA realization of multi-scroll chaotic oscillators , 2015, Commun. Nonlinear Sci. Numer. Simul..

[19]  Christos Volos,et al.  Coexistence of hidden chaotic attractors in a novel no-equilibrium system , 2017 .

[20]  Ludovico Minati,et al.  Experimental synchronization of chaos in a large ring of mutually coupled single-transistor oscillators: phase, amplitude, and clustering effects. , 2014, Chaos.

[21]  Julien Clinton Sprott,et al.  Some simple chaotic jerk functions , 1997 .

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

[23]  Christos Volos,et al.  A fractional system with five terms: analysis, circuit, chaos control and synchronization , 2018, International Journal of Electronics.

[24]  Chunbiao Li,et al.  Constructing Infinitely Many Attractors in a Programmable Chaotic Circuit , 2018, IEEE Access.

[25]  Guang Zeng,et al.  Hyperchaos and horseshoe in a 4D memristive system with a line of equilibria and its implementation , 2014, Int. J. Circuit Theory Appl..

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

[27]  Johan A. K. Suykens,et al.  Cellular Neural Networks, Multi-Scroll Chaos and Synchronization , 2005 .

[28]  Yuhua Xu,et al.  A new chaotic system without linear term and its impulsive synchronization , 2014 .

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

[30]  Ping Zhou,et al.  Hyperchaos, chaos, and horseshoe in a 4D nonlinear system with an infinite number of equilibrium points , 2014 .

[31]  Carlos Sánchez-López,et al.  Multiscroll floating gate–based integrated chaotic oscillator , 2013, Int. J. Circuit Theory Appl..

[32]  Tomas Gotthans,et al.  New class of chaotic systems with circular equilibrium , 2015 .

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

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

[35]  Pyung Hun Chang,et al.  Introduction and synchronization of a five-term chaotic system with an absolute-value term , 2013 .

[36]  Carlos Sánchez-López,et al.  Integrated circuit generating 3- and 5-scroll attractors , 2012 .

[37]  E. Tlelo-Cuautle,et al.  N-scroll chaotic attractors from saturated function series employing CCII+s , 2010 .

[38]  Kehui Sun,et al.  Bifurcations of Fractional-order Diffusionless Lorenz System , 2009 .

[39]  Luigi Fortuna,et al.  Nonideal Behavior of Analog Multipliers for Chaos Generation , 2016, IEEE Transactions on Circuits and Systems II: Express Briefs.

[40]  Bharathwaj Muthuswamy A Route to Chaos Using FPGAs : Volume I: Experimental Observations , 2015 .

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

[42]  Julien Clinton Sprott,et al.  Generalization of the simplest autonomous chaotic system , 2011 .

[43]  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.

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

[45]  G. A. Leonov,et al.  Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations , 2014, 1410.2016.

[46]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering , 1994 .

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

[48]  Julien Clinton Sprott,et al.  A Simple Chaotic Flow with a Plane of Equilibria , 2016, Int. J. Bifurc. Chaos.

[49]  Esteban Tlelo-Cuautle,et al.  Frequency scaling simulation of Chua's circuit by automatic determination and control of step-size , 2007, Appl. Math. Comput..

[50]  J. Sprott Elegant Chaos: Algebraically Simple Chaotic Flows , 2010 .

[51]  L. Faes,et al.  Atypical transistor-based chaotic oscillators: Design, realization, and diversity. , 2017, Chaos.

[52]  Viet-Thanh Pham,et al.  Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system , 2018, Int. J. Syst. Sci..

[53]  Luigi Fortuna,et al.  Essentials of Nonlinear Circuit Dynamics with MATLAB® and Laboratory Experiments , 2017 .