Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms

A novel hyperchaotic system with fractional-order (FO) terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.

[1]  Sundarapandian Vaidyanathan,et al.  Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities , 2014 .

[2]  T. Carroll A simple circuit for demonstrating regular and synchronized chaos , 1995 .

[3]  A. E. Matouk,et al.  Chaos, feedback control and synchronization of a fractional-order modified Autonomous Van der Pol–Duffing circuit , 2011 .

[4]  Eric Campos-Cantón,et al.  Chaotic attractors based on unstable dissipative systems via third-order differential equation , 2016 .

[5]  O. Rössler An equation for hyperchaos , 1979 .

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

[7]  Vinod Patidar,et al.  Bifurcation and chaos in simple jerk dynamical systems , 2005 .

[8]  Olfa Boubaker,et al.  On new chaotic and hyperchaotic systems: A literature survey , 2016 .

[9]  Zhouchao Wei,et al.  Hidden Hyperchaotic Attractors in a Modified Lorenz-Stenflo System with Only One Stable Equilibrium , 2014, Int. J. Bifurc. Chaos.

[10]  Mustafa Mamat,et al.  Numerical simulation chaotic synchronization of Chua circuit and its application for secure communication , 2013 .

[11]  Chun-Lai Li,et al.  A new hyperchaotic system and its generalized synchronization , 2014 .

[12]  Irene M. Moroz,et al.  Synchronization and Electronic Circuit Application of Hidden Hyperchaos in a Four-Dimensional Self-Exciting Homopolar Disc Dynamo without Equilibria , 2017, Complex..

[13]  L. Chua,et al.  Hyper chaos: Laboratory experiment and numerical confirmation , 1986 .

[14]  Sundarapandian Vaidyanathan,et al.  Analysis, Adaptive Control and Synchronization of a Novel 4-D Hyperchaotic Hyperjerk System via Backstepping Control Method , 2016 .

[15]  Viet-Thanh Pham,et al.  Bifurcation analysis and circuit realization for multiple-delayed Wang–Chen system with hidden chaotic attractors , 2016 .

[16]  Peng Li,et al.  A unique jerk system with hidden chaotic oscillation , 2016 .

[17]  Eric Campos-Cantón,et al.  Generation of chaotic attractors without equilibria via piecewise linear systems , 2017 .

[18]  George S. Tombras,et al.  A Novel Chaotic System without Equilibrium: Dynamics, Synchronization, and Circuit Realization , 2017, Complex..

[19]  Hans Peter Gottlieb,et al.  What is the Simplest Jerk Function that Gives Chaos , 1996 .

[20]  S. Vaidyanathan,et al.  Dynamical Analysis and FPGA Implementation of a Novel Hyperchaotic System and Its Synchronization Using Adaptive Sliding Mode Control and Genetically Optimized PID Control , 2017 .

[21]  Rongrong Wang,et al.  A new finding of the existence of hidden hyperchaotic attractors with no equilibria , 2014, Math. Comput. Simul..

[22]  Matthew Nicol,et al.  Generation of multi-scroll attractors without equilibria via piecewise linear systems. , 2017, Chaos.

[23]  Julien Clinton Sprott,et al.  A new class of chaotic circuit , 2000 .

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

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

[26]  A. Elwakil,et al.  On the stability of linear systems with fractional-order elements , 2009 .