Chaotic resonance: Hopping rates, spectra and signal-to-noise ratios

Kovaleva, Agnessa; Simiu, Emil
February 2000
AIP Conference Proceedings;2000, Vol. 502 Issue 1, p428
Academic Journal
We consider a noise-free bistable system with a low frequency signal and a secondary harmonic excitation that causes the system to experience chaotic motion with a broadband portion of the output spectrum. The signal-to-noise ratio (SNR) is defined on the basis of this broadband spectrum. We present the theoretical back-ground for approximate calculation of the hopping rate, the output spectra and SNR of the system. It is shown that, under a proper choice of the secondary excitation, the SNR can be enhanced. This phenomenon is referred to as chaotic resonance. We show similarities between results obtained for chaotic resonance on the one hand and classical stochastic resonance induced by random perturbations on the other. As an example, chaotic resonance in the Holmes-Brunsden oscillator is studied. © 2000 American Institute of Physics.


Related Articles

  • Overview: The constructive role of noise in fluctuation driven transport and scholastic resonance. Astumian, R. Dean; Moss, Frank // Chaos;Sep98, Vol. 8 Issue 3, p533 

    Studies the constructive role of noise in fluctuation driven transport and stochastic resonance. Mechanism by which noise and Brownian motion can facilitate transmission of information and help systems use chemical energy and nonequilibrium fluctuations to drive directed motion via a...

  • Constructive role of noise: Fast fluctuation asymptotics of transport in stochastic ratchets. Doeing, Charles R.; Dontcheva, Lubomira A.; Klosek, Malgorzata M. // Chaos;Sep98, Vol. 8 Issue 3, p643 

    Studies the constructive role of random noise fluctuations in the context of transport in stochastic resonance ratchets. Ratchet potentials; Characterization of the Markov process; Physical mechanism for particle transport under the influence of the mean zero fluctuating force.

  • Chaotic synchronization induced by exponentially correlated parametric noise. Lorenzo, M. N.; Pe´rez-Mun˜uzuri, V. // AIP Conference Proceedings;2000, Vol. 502 Issue 1, p387 

    The effect of colored noise on chaotic synchronization is studied for one-dimensional arrays of diffusively chaotic coupled Lorenz systems. An enhancement or a worsening of the synchronization has been observed as a function of the correlation time of the noise, the number of cells in the array,...

  • Sensitivity to Initial Conditions and Lyapunov Exponent of a Quasiperiodic System. Khovanov, I. A.; Khovanova, N. A.; Anishchenko, V. S.; McClintock, P. W. E. // Technical Physics;May2000, Vol. 45 Issue 5, p633 

    The dynamics of a quasiperiodic map is analyzed both in the presence and in the absence of weak noise. It is shown that, in the presence of weak noise, a strange chaotic attractor with a negative Lyapunov exponent and sensitive dependence of trajectories on the initial conditions can exist in...

  • Formation of a chaotic layer of nonlinear resonance by a two-frequency perturbation. Vecheslavov, V. V. // JETP Letters;6/25/96, Vol. 63 Issue 12, p1047 

    A new effect [V. V. Vecheslavov, Zh. Éksp. Teor. Fiz. 109, 2208 (1996) (JETP 82, 1190 (1996)]—the appearance of low-frequency secondary harmonics in the separatrix mapping of a system—is discussed in detail for the example of a pendulum with a two-frequency perturbation. It is...

  • Evidence of a nanomechanical resonator being driven into chaotic response via the Ruelle–Takens route. Scheible, Dominik V.; Erbe, Artur; Blick, Robert H.; Corso, Gilberto // Applied Physics Letters;9/2/2002, Vol. 81 Issue 10, p1884 

    Nanomechanical resonators, of importance for signal filtering and transduction, are investigated within the limit of extreme nonlinear excitation. The Ruelle-Takens route establishes the transition of a system into chaos with n frequencies present. By providing a set of three sources, this...

  • The effect of topology on neural networks with unstable memories. Johnson, S.; Marro, J.; Torres, J. J. // AIP Conference Proceedings;2007, Vol. 887 Issue 1, p261 

    The article provides information on the effect of topology on neural networks with unstable memories. The researchers studied an attractor neural network where a noise parameter causes instabilities of the memory stored patterns. The consequence of noise provides with three phases like a...

  • Noise can prevent onset of chaos in spatiotemporal population dynamics. Petrovskii, S.; Morozov, A.; Malchow, H.; Sieber, M. // European Physical Journal B -- Condensed Matter;Nov2010, Vol. 78 Issue 2, p253 

    Many theoretical approaches predict the dynamics of interacting populations to be chaotic but that has very rarely been observed in ecological data. It has therefore risen a question about factors that can prevent the onset of chaos by, for instance, making the population fluctuations...

  • A chaotically driven model climate: extreme events and snapshot attractors. Bódai, T.; Károlyi, Gy.; Tél, T.; Kurths, J.; Redondo, J. M. // Nonlinear Processes in Geophysics;2011, Vol. 18 Issue 5, p573 

    In a low-order chaotic global atmospheric circulation model the effects of deterministic chaotic driving are investigated. As a result of driving, peak-over-threshold type extreme events, e.g. cyclonic activity in the model, become more extreme, with increased frequency of recurrence. When the...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics