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The dynamical systems in real world are inevitably affected by noise, causing various random behaviors. Currently, the research on the stochastic dynamics of noise driven systems has become a hot topic. This paper aims to explore the stochastic dynamics of the FitzHugh-Nagumo (FHN) neuronal system driven by Lévy noise. The research mainly includes the dynamical response of the FHN neuronal system and the deep learning-based parameter estimation.
The relevant basic theory of Lévy noise is presented. The Lévy stable distribution is defined. The impacts of the stability index and the skewness coefficient on the probability density function of Lévy stable distribution are analyzed. The Chambers-Mallows-Stuck method for generating the random numbers of Lévy distribution is introduced.
By using the Euler-Maruyama method for numerically simulating the FHN model, the dynamic characteristics of the FHN neuronal system driven by Lévy noise is investigated. It is found that the change of external input current, periodic signal amplitude and noise intensity can change the state of the neuronal system. In addition, changing the parameters of the deterministic system leads to bifurcation phenomena in the stochastic system. The parameters of the driven Lévy noise can induce stochastic bifurcation phenomena and affect the stability of the system.
In order to more accurately estimate the parameters of the FHN neuronal system driven by Lévy noise, and further analyze and control the stochastic system, a parameter estimation neural network (PENN) is proposed, where a long short-term memory neural network and a fully connected neural network are combined to estimate the parameters from a sample trajectory. The precision and accuracy of the PENN are evaluated by the metrics including the mean, standard deviation and mean absolute error of the estimations. Numerical experiments have verified that the PENN can estimate the parameters of the system with high speed, precision and accuracy.
| Секция конференции | Методы искусственного интеллекта и машинного обучения |
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