scholarly journals Dynamical systems: an integrable kernel for resonance effects

2009 ◽  
Vol 1 (1) ◽  
Author(s):  
J. Kennety
Keyword(s):  
Dynamical Systems ◽  
Resonance Effects ◽  
Integrable Kernel

ON LOGARITHMIC ASYMPTOTICS OF STOCHASTIC RESONANCE FREQUENCIES

2003 ◽  
Vol 03 (01) ◽  
pp. 55-71
Author(s):  
S. C. CARMONA ◽  
M. I. FREIDLIN
Keyword(s):  
Dynamical Systems ◽  
Stochastic Resonance ◽  
Small Amplitude ◽  
Large Deviation ◽  
Large Deviation Theory ◽  
Resonance Effects ◽  
Resonance Frequencies ◽  
Logarithmic Asymptotics ◽  
The Relationship ◽  
Deviation Theory

Stochastic resonance effects due to arbitrarily small amplitude deterministic perturbations in dynamical systems with noise are studied. The concept of Log-Asymptotic Resonance Frequency is introduced and the relationship between its existence and some types of symmetries in the stochastic system is established; the spectrum of this kind of frequencies is determined. These symmetries are defined through the quasi-deterministic approximation of the system. The large deviation theory gives the basic machinery for this analysis.

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