FPGA implementation of a chaotic oscillator using RK4 method

The dual deterministic-stochastic behavior of chaotic systems (CS) makes them extremely interesting in electronic engineering as CS may replace noise sources in different applications. Consequently it is convenient to have hardware implementations for both, analog and digital versions. Discrete components, Micro Controllers, Digital Signal Processors (DSP) and Field Programmable Gate Arrays (FPGAs) are possible choices.

[1]  Hilda A. Larrondo,et al.  Generalized Statistical Complexity Measure , 2010, Int. J. Bifurc. Chaos.

[2]  A. Dandache,et al.  Real-time FPGA implementation of Lorenz's chaotic generator for ciphering telecommunications , 2009, 2009 Joint IEEE North-East Workshop on Circuits and Systems and TAISA Conference.

[3]  J. Butcher.  Numerical methods for ordinary differential equations , 2003 .

[4]  Sergio Callegari,et al.  Chaos-based FM signals: application and implementation issues , 2003 .

[5]  Hilda A. Larrondo,et al.  Versatile DSP-based chaotic communication system , 2001 .

[6]  Oliver Lundqvist,et al.  Numerical Methods for Ordinary Differential Equations , 2013, An Introduction to Numerical Methods and Analysis 3e.

[7]  Sergio Callegari,et al.  A CMOS tailed tent map for the generation of uniformly distributed chaotic sequences , 1997, Proceedings of 1997 IEEE International Symposium on Circuits and Systems. Circuits and Systems in the Information Age ISCAS '97.

[8]  Takashi Matsumoto,et al.  A chaotic attractor from Chua's circuit , 1984 .

[9]  Osvaldo A. Rosso,et al.  Randomizing nonlinear maps via symbolic dynamics , 2008 .

[10]  Adda Ali-Pacha,et al.  Lorenz’s attractor applied to the stream cipher (Ali-Pacha generator) , 2007 .

[11]  O. Rössler.  An equation for continuous chaos , 1976 .

[12]  Guanrong Chen,et al.  Bifurcation Analysis of Chen's equation , 2000, Int. J. Bifurc. Chaos.

[13]  Hilda A. Larrondo,et al.  Generalized Statistical Complexity Measure: A New Tool for Dynamical Systems , 2008 .

[14]  Riccardo Rovatti,et al.  Experimental verification of enhanced electromagnetic compatibility in chaotic FM clock signals , 2000, 2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353).

[15]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[16]  Peter Lee,et al.  Lorenz chaotic model using Filed Programmable Gate Array (FPGA) , 2002, The 2002 45th Midwest Symposium on Circuits and Systems, 2002. MWSCAS-2002..

[17]  Songsong Lu,et al.  Attractors for nonautonomous reaction-diffusion systems with symbols without strong translation compactness , 2007, Asymptot. Anal..

[18]  Riccardo Rovatti,et al.  Chaotic complex spreading sequences for asynchronous DS-CDMA. I. System modeling and results , 1997 .

[19]  O A Rosso,et al.  Quantifiers for randomness of chaotic pseudo-random number generators , 2008, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.