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Effects of Lévy noise on the Fitzhugh-Nagumo model: A perspective on the maximal likely trajectories.
J Theor Biol 2019; 480:166-174JT

Abstract

This paper considers about the escape paths of the FitzHugh-Nagumo neural system driven by symmetric α-stable Lévy noise (non-Gaussian noise). The existing research has shown that noise can make this system produce a spike pulse, which corresponds to a state transition. To analyze the effects of Lévy noise on the state transition, a novel statistical quantity called maximal likely trajectory, which is obtained by recording the maximizer of the probability density function at every moment, is used to characterize the escape paths of the equilibrium and revel the relationship between state transition and noise intensity or Lévy motion index. The numerical experiments show that for fixed Lévy motion index, the larger noise intensity can promote this neural system to an excitatory state. In addition, the influence of Lévy motion index on the state transition depends on the selection of noise intensity in this neural system. Meanwhile, as a comparison, the case driven by Brownian motion (Gaussian noise) is also taken into account, which shows that in some situations Lévy noise makes the FitzHugh-Nagumo system excited in shorter time. In addition, the maximal likely trajectory provides us with a new perspective to show the existence of a separatrix in the stochastic setting of the FitzHugh-Nagumo model and also depict the rough shape of the middle part of this separatrix.

Authors+Show Affiliations

School of Science, Hubei University of Technology, Wuhan 430068, China; Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China.School of Science, Wuhan University of Technology, Wuhan 430070, China; Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China. Electronic address: ziyinghe@hust.edu.cn.School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China; Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China.Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA.Department of Physics, Humboldt University of Berlin, Newtonstrate 15, Berlin 12489, Germany.Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA.

Pub Type(s)

Journal Article

Language

eng

PubMed ID

31419442

Citation

Cai, Rui, et al. "Effects of Lévy Noise On the Fitzhugh-Nagumo Model: a Perspective On the Maximal Likely Trajectories." Journal of Theoretical Biology, vol. 480, 2019, pp. 166-174.
Cai R, He Z, Liu Y, et al. Effects of Lévy noise on the Fitzhugh-Nagumo model: A perspective on the maximal likely trajectories. J Theor Biol. 2019;480:166-174.
Cai, R., He, Z., Liu, Y., Duan, J., Kurths, J., & Li, X. (2019). Effects of Lévy noise on the Fitzhugh-Nagumo model: A perspective on the maximal likely trajectories. Journal of Theoretical Biology, 480, pp. 166-174. doi:10.1016/j.jtbi.2019.08.010.
Cai R, et al. Effects of Lévy Noise On the Fitzhugh-Nagumo Model: a Perspective On the Maximal Likely Trajectories. J Theor Biol. 2019 Nov 7;480:166-174. PubMed PMID: 31419442.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Effects of Lévy noise on the Fitzhugh-Nagumo model: A perspective on the maximal likely trajectories. AU - Cai,Rui, AU - He,Ziying, AU - Liu,Yancai, AU - Duan,Jinqiao, AU - Kurths,Jürgen, AU - Li,Xiaofan, Y1 - 2019/08/13/ PY - 2019/06/19/received PY - 2019/08/11/revised PY - 2019/08/13/accepted PY - 2019/8/17/pubmed PY - 2019/8/17/medline PY - 2019/8/17/entrez KW - Fitzhugh–Nagumo model KW - Maximal likely trajectory KW - Non-Gaussian Lévy motion KW - Probability density function KW - Stochastic dynamics SP - 166 EP - 174 JF - Journal of theoretical biology JO - J. Theor. Biol. VL - 480 N2 - This paper considers about the escape paths of the FitzHugh-Nagumo neural system driven by symmetric α-stable Lévy noise (non-Gaussian noise). The existing research has shown that noise can make this system produce a spike pulse, which corresponds to a state transition. To analyze the effects of Lévy noise on the state transition, a novel statistical quantity called maximal likely trajectory, which is obtained by recording the maximizer of the probability density function at every moment, is used to characterize the escape paths of the equilibrium and revel the relationship between state transition and noise intensity or Lévy motion index. The numerical experiments show that for fixed Lévy motion index, the larger noise intensity can promote this neural system to an excitatory state. In addition, the influence of Lévy motion index on the state transition depends on the selection of noise intensity in this neural system. Meanwhile, as a comparison, the case driven by Brownian motion (Gaussian noise) is also taken into account, which shows that in some situations Lévy noise makes the FitzHugh-Nagumo system excited in shorter time. In addition, the maximal likely trajectory provides us with a new perspective to show the existence of a separatrix in the stochastic setting of the FitzHugh-Nagumo model and also depict the rough shape of the middle part of this separatrix. SN - 1095-8541 UR - https://www.unboundmedicine.com/medline/citation/31419442/Effects_of_Lévy_noise_on_the_FitzHugh-Nagumo_model:_A_perspective_on_the_maximal_likely_trajectories L2 - https://linkinghub.elsevier.com/retrieve/pii/S0022-5193(19)30322-4 DB - PRIME DP - Unbound Medicine ER -