FPGA Implementation of X- and Heart-shapes Controllable Multi-Scroll Attractors

This paper proposes new multi-scrolls chaotic systems which is called the X-shape. The purpose is to have more complex systems and flexible ranges of the chaotic behavior. The proposed X-shape is a combination between V-shape and Λ-shape. This paper also represents the Heart-shape which considered a special case of the X-shape. The system complexity has been measured by MLE and compared with V-shape system. It shows lager MLE on the side of X-shape. In addition, the effect of changing system parameters has been discussed and compared with V-shape. Finally, a fully hardware implantation on FPGA has been proposed using Nexys 4 Artix-7 FPGA XC7A100T with optimum resources and the experimental results are provided.

[1]  Ahmad Taher Azar,et al.  FPGA implementation of two fractional order chaotic systems , 2017 .

[2]  Mohammed Affan Zidan,et al.  The effect of numerical techniques on differential equation based chaotic generators , 2011, ICM 2011 Proceeding.

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

[4]  Jacques M. Bahi,et al.  FPGA Design for Pseudorandom Number Generator Based on Chaotic Iteration used in Information Hiding Application , 2013, ArXiv.

[5]  Abbas Dandache,et al.  A new auto-switched chaotic system and its FPGA implementation , 2013, Commun. Nonlinear Sci. Numer. Simul..

[6]  J. Yorke,et al.  Chaos: An Introduction to Dynamical Systems , 1997 .

[7]  Ihsan Pehlivan,et al.  Implementation of FPGA-based real time novel chaotic oscillator , 2014 .

[8]  J. Rogers.  Chaos , 1876 .

[9]  Wimol San-Um,et al.  Digital Chaotic Signal Generator Using Robust Chaos in Compound Sinusoidal Maps , 2014, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[10]  Luis Gerardo de la Fraga,et al.  Engineering Applications of FPGAs , 2016 .

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

[12]  Sundarapandian Vaidyanathan,et al.  Chaos Modeling and Control Systems Design , 2014, Chaos Modeling and Control Systems Design.

[13]  Sundarapandian Vaidyanathan,et al.  Generalized Projective Synchronization of Vaidyanathan Chaotic System via Active and Adaptive Control , 2016 .

[14]  Ahmed G. Radwan,et al.  Generalized Hardware Post‐processing Technique for Chaos‐Based Pseudorandom Number Generators , 2013 .

[15]  Khaled N. Salama,et al.  Hardware stream cipher with controllable chaos generator for colour image encryption , 2014, IET Image Process..

[16]  E. Tlelo-Cuautle,et al.  FPGA realization of a chaotic communication system applied to image processing , 2015 .

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

[18]  Ahmed S. Elwakil,et al.  1-d digitally-Controlled multiscroll Chaos Generator , 2007, Int. J. Bifurc. Chaos.

[19]  Patrick Coirault,et al.  Design and FPGA-realization of a self-synchronizing chaotic decoder in the presence of noise , 2012 .

[20]  Mohammed Affan Zidan,et al.  Controllable V-Shape multiscroll Butterfly Attractor: System and Circuit Implementation , 2012, Int. J. Bifurc. Chaos.

[21]  Lei Chen,et al.  Circuit implementation and model of a new multi‐scroll chaotic system , 2014, Int. J. Circuit Theory Appl..

[22]  Ahmad Taher Azar,et al.  Fractional controllable multi-scroll V-shape attractor with parameters effect , 2017, 2017 6th International Conference on Modern Circuits and Systems Technologies (MOCAST).

[23]  Marius-F. Danca,et al.  Hidden transient chaotic attractors of Rabinovich–Fabrikant system , 2016, 1604.04055.

[24]  吴文娟,et al.  A novel hyperchaos evolved from three dimensional modified Lorenz chaotic system , 2007 .