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Global dynamics of a stochastic neuronal oscillator
1Hokkaido University School of Medicine, North 15, West 7, Kita-ku, Sapporo 060-8638, Japan and PRESTO, Japan Science and Technology Agency (JST), 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 17, 2013
Summary
This study analyzes impulse-driven stochastic neuronal oscillators. We found that past neuronal activity, influenced by relaxation rate, noise, and input parameters, determines the oscillator
Area of Science:
- Computational Neuroscience
- Nonlinear Dynamics
- Stochastic Processes
Background:
- Nonlinear oscillators model periodically firing neurons and share dynamics with biological oscillations like cardiac cells.
- Understanding neuronal oscillator responses to impulses is crucial for modeling brain activity.
Purpose of the Study:
- Analyze the global dynamics of impulse-driven stochastic neuronal oscillators.
- Investigate the influence of relaxation rate, intrinsic noise, and input parameters on oscillator behavior.
- Relate oscillator dynamics to spike generation and interspike intervals.
Main Methods:
- Utilized a Markov operator to model density evolution and phase transitions of neuronal oscillators.
- Constructed Markov operators for both finite and infinite relaxation rates, focusing on limit cycle dynamics.
- Analyzed the response to time-varying impulses using products of Markov operators.
Main Results:
- The response of stochastic neuronal oscillators to impulses is described by a product of Markov operators.
- Calculated the number of spikes between impulses to link dynamics to spike rate and interspike interval density.
- Decomposed Markov operators into stationary and transient components to analyze differences in spike rates based on past activity.
Conclusions:
- The duration of past neuronal activity significantly impacts oscillator dynamics.
- Relaxation rate, noise strength, and input parameters collectively govern the dependence on past activity.
- This framework provides insights into how neuronal oscillators integrate past activity to generate future responses.
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