Chaotic dynamics of a frequency-modulated microwave oscillator with time-delayed feedback.

We present a chaotic frequency-modulated microwave source that is governed by a simple, first-order nonlinear delay differential equation. When a sinusoidal nonlinearity is incorporated, the dynamical behaviors range from fixed-point to periodic to chaotic, depending on the feedback strength. When the sinusoidal nonlinearity is replaced by a binary nonlinearity, the system exhibits a complex periodic attractor with no fixed-point solution.

[1]  Alan V. Oppenheim,et al.  Synchronization of Lorenz-based chaotic circuits with applications to communications , 1993 .

[2]  L. Kocarev,et al.  Chaos-based random number generators. Part II: practical realization , 2001 .

[3]  Thomas L Carroll.  Chaotic system for self-synchronizing Doppler measurement. , 2005, Chaos.

[4]  J..  CHAOTIC ATTRACTORS OF AN INFINITE-DIMENSIONAL DYNAMICAL SYSTEM , 2002 .

[5]  Julien Clinton Sprott,et al.  A simple chaotic delay differential equation , 2007 .

[6]  L. Kocarev,et al.  Chaos-based random number generators-part I: analysis [cryptography] , 2001 .

[7]  Rajarshi Roy,et al.  Using synchronization for prediction of high-dimensional chaotic dynamics. , 2008, Physical review letters.

[8]  Firdaus E. Udwadia,et al.  An efficient QR based method for the computation of Lyapunov exponents , 1997 .

[9]  M. Ghil,et al.  Boolean delay equations: A simple way of looking at complex systems , 2006, nlin/0612047.

[10]  Jia-Ming Liu,et al.  Chaotic radar using nonlinear laser dynamics , 2004, IEEE Journal of Quantum Electronics.

[11]  D. Gauthier,et al.  High-speed chaos in an optical feedback system with flexible timescales , 2003, IEEE Journal of Quantum Electronics.

[12]  Ned J Corron,et al.  A matched filter for chaos. , 2010, Chaos.

[13]  S. Pethel,et al.  High-precision ranging using a chaotic laser pulse train , 2001 .

[14]  J.H.B. Deane,et al.  Improvement of power supply EMC by chaos , 1996 .

[15]  Laurent Larger,et al.  Chaotic breathers in delayed electro-optical systems. , 2005, Physical review letters.

[16]  Adonis Bogris,et al.  Chaos-based communications at high bit rates using commercial fibre-optic links , 2006, SPIE/OSA/IEEE Asia Communications and Photonics.

[17]  K. Alan Shore,et al.  Dual-channel chaotic optical communications using external-cavity semiconductor lasers , 2004 .

[18]  J. Gleeson,et al.  Truly random number generator based on turbulent electroconvection , 2002 .

[19]  W. T. Rhodes,et al.  Bandpass chaotic dynamics of electronic oscillator operating with delayed nonlinear feedback , 2002 .

[20]  Gabriel Thomas,et al.  Assessment of chaos-based FM signals for range-Doppler imaging , 2003 .

[21]  A. Uchida,et al.  Fast physical random bit generation with chaotic semiconductor lasers , 2008 .

[22]  Greg M. Bernstein,et al.  Secure random number generation using chaotic circuits , 1990 .

[23]  K. Ikeda,et al.  High-dimensional chaotic behavior in systems with time-delayed feedback , 1987 .

[24]  Luigi Fortuna,et al.  Chaotic pulse position modulation to improve the efficiency of sonar sensors , 2003, IEEE Trans. Instrum. Meas..

[25]  Roy,et al.  Communication with chaotic lasers , 1998, Science.

[26]  Michael Schanz,et al.  Analytical and numerical investigations of the phase-locked loop with time delay. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Gianluca Mazzini,et al.  Interference minimisation by auto-correlation shaping in asynchronous DS-CDMA systems: chaos-based spreading is nearly optimal , 1999 .