Optimizing criterion for the upper limit of the signal response of brain neurons

ABSTRACT

In a model of signal transmission between brain neurons, the Lyapunov functions associated with the “no signal” solution are positive and have a negative derivative with respect to the response. The solution is stable for a response range. Noise added to signal transmission and response enhances stability by allowing the system to escape tricky equilibria. It amplifies weak signals, improves detection and distinction of significant signals from background noise, and generates appropriate and adaptive responses to detected signals. It causes random fluctuations, allowing more parameter values to be tried out and thus optimizing the behavior of the system, enabling it to transmit and respond effectively to signals in the presence of the variability inherent in biological networks. The deterministic model is thus enhanced by its stochastic extension.

KEYWORDS:

• Extinction
• global stability
• Lyapunov stability
• mean-square
• neural networks

JEL CLASSIFICATION:

• 3A34
• 3A60
• 37C75

Acknowledgments

Our sincere thanks to two reviewers for their helpful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors reported there is no funding associated with the work featured in the article.