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Extending stochastic resonance for neuron models to general Lévy noise
1Probability and Statistics Department, University of Sheffield, Sheffield, UK. D.Applebaum@sheffield.ac.uk
IEEE Transactions on Neural Networks
|October 14, 2009
Summary
This study extends stochastic resonance (SR) findings to general Lévy noise models by controlling large noise jumps, enabling stochastic models to approach deterministic ones. This broadens the applicability of SR in neural modeling.
Area of Science:
- Computational Neuroscience
- Stochastic Processes
- Nonlinear Dynamics
Background:
- Stochastic resonance (SR) has been demonstrated in neural models with specific noise types.
- Previous work by Patel and Kosko (2008) established SR for additive Lévy noise with finite second moments.
- A limitation of prior models was the constraint on noise properties.
Purpose of the Study:
- To extend the demonstration of stochastic resonance to more general Lévy noise models.
- To remove the constraint of finite second moments for Lévy noise in SR studies.
- To investigate the role of "large jump" discontinuities in noise-induced phenomena.
Main Methods:
- Analysis of general Lévy noise models without finite second moment constraints.
- Control of "large jump" discontinuities in the noise.
- Demonstration of the stochastic model tending towards a deterministic one as noise intensity decreases.
- Application of a "forbidden intervals" theorem.
Main Results:
- Stochastic resonance is shown to occur for general Lévy noise models.
- The previously established SR results are extended beyond the finite second moment constraint.
- "Large jump" noise discontinuities can be managed to ensure convergence to deterministic behavior.
Conclusions:
- The findings broaden the theoretical framework for stochastic resonance in neural systems.
- The study validates the extension of SR to a wider class of noise processes.
- This work provides a more robust understanding of noise-driven phenomena in computational neuroscience.
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