Chaotic systems that are robust to added noise.

While added noise can destroy synchronization in synchronized chaotic systems, it was shown that some chaotic systems were not sensitive to added noise. In this paper, the mechanism for this noise resistance is explored. It is seen that part of the chaotic system acts like it is resonant, reducing the noise sensitivity of the system. By comparing to a model of a neuron, it is speculated that similar mechanisms may also be present in biological systems.

[1]  Ljupco Kocarev,et al.  General approach for chaotic synchronization with applications to communication. , 1995, Physical review letters.

[2]  Lakshmanan,et al.  Transmission of signals by synchronization in a chaotic Van der Pol-Duffing oscillator. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  S Boccaletti,et al.  Noise-enhanced synchronization of homoclinic chaos in a CO2 laser. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Wolfgang Schwarz,et al.  Noise performance of chaotic communication systems , 2000 .

[5]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .

[6]  K. D. Minto.  On coprime factorizations for parallel interconnections of systems , 1993 .

[7]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[8]  T L Carroll.  Noise-resistant chaotic synchronization. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  M C Eguia,et al.  Information transmission and recovery in neural communications channels. , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  Parlitz,et al.  Encoding messages using chaotic synchronization. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  S Boccaletti,et al.  Constructive effects of noise in homoclinic chaotic systems. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Leon O. Chua,et al.  Synchronization of Chua's circuits with time-varying channels and parameters , 1996 .

[13]  O. Rössler.  The Chaotic Hierarchy , 1983 .

[14]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[15]  Michael Peter Kennedy,et al.  The role of synchronization in digital communications using chaos. I . Fundamentals of digital communications , 1997 .

[16]  Jürgen Kurths,et al.  Noise-enhanced phase synchronization of chaotic oscillators. , 2002, Physical review letters.

[17]  C. Williams.  Chaotic communications over radio channels , 2001 .

[18]  Jürgen Kurths,et al.  Noise-induced phase synchronization and synchronization transitions in chaotic oscillators. , 2002, Physical review letters.

[19]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[20]  Hassan K. Khalil,et al.  Singular perturbation methods in control : analysis and design , 1986 .

[21]  Thomas L. Carroll,et al.  Noise-robust synchronized chaotic communications , 2001 .