Changes in the dynamical behavior of nonlinear systems induced by noise

PS Landa, PVE McClintock - Physics Reports, 2000 - Elsevier
Weak noise acting upon a nonlinear dynamical system can have far-reaching
consequences. The fundamental underlying problem–that of large deviations of a nonlinear …

Stable infinite variance fluctuations in randomly amplified Langevin systems

H Takayasu, AH Sato, M Takayasu - Physical Review Letters, 1997 - APS
A general discrete stochastic process involving random amplification with additive external
noise is analyzed theoretically and numerically. Necessary and sufficient conditions to …

Transition from local to global phase synchrony in small world neural network and its possible implications for epilepsy

B Percha, R Dzakpasu, M Żochowski, J Parent - Physical Review E—Statistical …, 2005 - APS
Temporal correlations in the brain are thought to have very dichotomous roles. On one hand
they are ubiquitously present in the healthy brain and are thought to underlie feature binding …

Noise-enhanced phase synchronization of chaotic oscillators

C Zhou, J Kurths, IZ Kiss, JL Hudson - Physical review letters, 2002 - APS
The effects of noise on phase synchronization (PS) of coupled chaotic oscillators are
explored. In contrast to coupled periodic oscillators, noise is found to enhance phase …

Dynamic numerical models of stock market price: from microscopic determinism to macroscopic randomness

AH Sato, H Takayasu - Physica A: Statistical Mechanics and its Applications, 1998 - Elsevier
A variant of threshold dynamics is introduced to model the behaviors of a large assembly of
dealers in a stock market. Although the microscopic evolution dynamics is deterministic the …

Constructive effects of noise in homoclinic chaotic systems

CS Zhou, J Kurths, E Allaria, S Boccaletti, R Meucci… - Physical Review E, 2003 - APS
Many chaotic oscillators have coherent phase dynamics but strong fluctuations in the
amplitudes. At variance with such a behavior, homoclinic chaos is characterized by quite …

On the unfolding of a blowout bifurcation

P Ashwin, PJ Aston, M Nicol - Physica D: Nonlinear Phenomena, 1998 - Elsevier
Suppose a chaotic attractor A in an invariant subspace loses stability on varying a
parameter. At the point of loss of stability, the most positive Lyapunov exponent of the natural …

Asymptotic power law of moments in a random multiplicative process with weak additive noise

H Nakao - Physical review E, 1998 - APS
It is well known that a random multiplicative process with weak additive noise generates a
power-law probability distribution. It has recently been recognized that this process exhibits …

Noise promotes species diversity in nature

YC Lai, YR Liu - Physical review letters, 2005 - APS
Species diversity in nature is accomplished by coexistence. In a spatial environment, inferior
but rapidly moving species can coexist with superior but relatively stationary species. Recent …

Robustness and stability of synchronized chaos: An illustrative model

MM Sushchik, NF Rulkov… - IEEE Transactions on …, 1997 - ieeexplore.ieee.org
Synchronization of two chaotic systems is not guaranteed by having only negative
conditional or transverse Lyapunov exponents. If there are transversally unstable periodic …