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Stochastic resonance in a linear system: An exact solution.

Héctor Calisto1, Fernando Mora, Enrique Tirapegui

  • 1Departamento de Física, Facultad de Ciencias, Universidad de Tarapacá Casilla 7-D, Arica, Chile. hcalisto@uta.cl

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
PubMed
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This study demonstrates stochastic resonance in a non-multistable linear system with multiplicative noise. Even with noise of a definite sign, signal amplification occurs, proving the effect

Area of Science:

  • Nonlinear Dynamics
  • Stochastic Processes
  • Signal Processing

Background:

  • Stochastic resonance (SR) is typically observed in multistable systems, amplifying weak signals via noise.
  • The role of noise in non-multistable systems, especially with multiplicative and signed noise, remains less explored.

Purpose of the Study:

  • To investigate the occurrence of stochastic resonance in a non-multistable linear system.
  • To analyze the impact of multiplicative colored noise, including noise with a definite sign, on signal amplification.

Main Methods:

  • Utilized functional integral techniques to derive an exact analytical expression for the mean value.
  • Employed numerical studies to analyze the system's response and confirm stochastic resonance.
  • Considered a linear system driven by a periodic signal and subjected to multiplicative noise.

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Main Results:

  • Demonstrated the phenomenon of stochastic resonance in a non-multistable linear system.
  • Confirmed that signal amplification can occur even when the noise component has a definite sign.
  • Validated the findings through numerical simulations based on derived analytical expressions.

Conclusions:

  • Stochastic resonance is not limited to multistable systems and can occur in simpler linear configurations.
  • The presence of multiplicative noise, even with a specific sign, can induce or enhance stochastic resonance.
  • This research broadens the understanding of stochastic resonance applicability to more general noise types and systems.