Lévy noise induced stochastic resonance in an FHN model

Science China Technological Sciences - Tập 59 Số 3 - Trang 371-375 - 2016
ZhanQing Wang1, Yong Xu1, Hui Yang2
1Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, China
2Department of Life Sciences, Northwestern Polytechnical University, Xi’an, China

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Tài liệu tham khảo

Fitzhugh R. Thresholds and plateaus in the Hodgkin-Huxley nerve equations. J Gen Physiol, 1960, 43: 867–896

Nagumo J, Arimoto S, Yoshizawa S. An active pulse transmission line simulating nerve axon. P IRE, 1962, 50: 2061–2070

Hodgkin A L, Huxley A F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol, 1952, 117: 500–544

Wang H X, Wang Q Y, Zheng Y H. Bifurcation analysis for Hindmarsh-Rose neuronal model with time-delayed feedback control and application to chaos control. Sci China Tech Sci, 2014, 57: 872–878

Sun X J, Shi X. Effects of channel blocks on the spiking regularity in clustered neuronal networks. Sci China Tech Sci, 2014, 57: 879–884

Alarcón T, Pérez-Madrid A, Rubí J M. Stochastic resonance in nonpotential systems. Phys Rev E, 1998, 57: 4979–4985

Lindner B, Schimansky-Geier L. Analytical approach to the stochastic FitzHugh-Nagumo system and coherence resonance. Phys Rev E, 1999, 60: 7270–7276

Longtin A. Stochastic resonance in neuron models. J Stat Phys, 1993, 70: 309–327

Collins J J, Chow C C, Imhoff T T. Stochastic resonance without tuning. Nature, 1995, 376: 236–238

Benzi R, Sutera A, Vulpiani A. The mechanism of stochastic resonance. J Phys A-Math Gen, 1981, 14: L453–L457

Wiesenfeld K, Moss F. Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs. Nature, 1995, 373: 33–36

Douglass J K, Wilkens L, Pantazelou E, et al. Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance. Nature, 1993, 365: 337–340

Zhang X F, Hu N Q, Hu L, et al. Multi-scale bistable stochastic resonance array: A novel weak signal detection method and application in machine fault diagnosis. Sci China Tech Sci, 2013, 56: 2115–2123

Xu Y, Wu J, Zhang H Q, et al. Stochastic resonance phenomenon in an underdamped bistable system driven by weak asymmetric dichotomous noise. Nonlinear Dynam, 2012, 70: 531–539

Zhang H Q, Yang T T, Xu Y, et al. Parameter dependence of stochastic resonance in the FitzHugh-Nagumo neuron model driven by trichotomous noise. Eur Phys J B, 2015, 88: 1–5

He Z Y, Zhou Y R. Vibrational and Stochastic Resonance in the FitzHugh-Nagumo Neural Model with Multiplicative and Additive Noise. Chin Phys Lett, 2011, 28:110505

Xu Y, Li J J, Feng J, et al. Lévy noise-induced stochastic resonance in a bistable system. Eur Phys J B, 2013, 86: 1–7

Li X L, Ning L J. Stochastic resonance in FizHugh-Nagumo model driven by multiplicative signal and non-Gaussian noise. Ind J Phys, 2015, 89: 189–194

Sun X J, Lu Q S. Non-gaussian colored noise optimized spatial coherence of a hodgkin-huxley neuronal network. Chin Phys Lett, 2014, 31: 020502

Xu Y, Feng J, Xu W, et al. Probability density transitions in the FizHugh-Nagumo model with Lévy noise. CMES-Comp Model Eng, 2015, 106: 309–322

Xu Y, Feng J, Li J J, et al. Lévy noise induced switch in the gene transcriptional regulatory system. Chaos, 2013, 23: 013110

Xu Y, Feng J, Li J J, et al. Stochastic bifurcation for a tumor–immune system with symmetric Lévy noise. Physica A, 2013, 392: 4739–4748

Janicki A, Weron A. Simulation and Chaotic Behavior of Alpha-Stable Stochastic Processes. New York: Marcel Dekker, 1994

Chambers J M, Mallows C L, Stuck B W. A method for simulating stable random variables. J Am Stat, 1976, 71: 340–344

Weron R. On the Chambers–Mallows–Stuck method for simulating skewed stable random variables. Stat Probabil Lett, 1996, 28: 165–171

Mitaim S, Kosko B. Adaptive stochastic resonance. P IEEE, 1998, 86: 2152–2183