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Stochastic modeling of the firing activity of coupled neurons periodically driven
1.  Istituto per le Applicazioni del Calcolo CNR, Napoli, Italy 
2.  Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, Napoli 
References:
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References:
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Massimiliano Tamborrino. Approximation of the first passage time density of a Wiener process to an exponentially decaying boundary by twopiecewise linear threshold. Application to neuronal spiking activity. Mathematical Biosciences & Engineering, 2016, 13 (3) : 613629. doi: 10.3934/mbe.2016011 
[2] 
Marie Levakova. Effect of spontaneous activity on stimulus detection in a simple neuronal model. Mathematical Biosciences & Engineering, 2016, 13 (3) : 551568. doi: 10.3934/mbe.2016007 
[3] 
Meiqiao Ai, Zhimin Zhang, Wenguang Yu. First passage problems of refracted jump diffusion processes and their applications in valuing equitylinked death benefits. Journal of Industrial and Management Optimization, 2022, 18 (3) : 16891707. doi: 10.3934/jimo.2021039 
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Omer Gursoy, Kamal Adli Mehr, Nail Akar. Steadystate and first passage time distributions for waiting times in the $ MAP/M/s+G $ queueing model with generally distributed patience times. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021078 
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Angelica Pachon, Federico Polito, Costantino Ricciuti. On discretetime semiMarkov processes. Discrete and Continuous Dynamical Systems  B, 2021, 26 (3) : 14991529. doi: 10.3934/dcdsb.2020170 
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Vincent Renault, Michèle Thieullen, Emmanuel Trélat. Optimal control of infinitedimensional piecewise deterministic Markov processes and application to the control of neuronal dynamics via Optogenetics. Networks and Heterogeneous Media, 2017, 12 (3) : 417459. doi: 10.3934/nhm.2017019 
[7] 
Qiuying Li, Lifang Huang, Jianshe Yu. Modulation of firstpassage time for bursty gene expression via random signals. Mathematical Biosciences & Engineering, 2017, 14 (5&6) : 12611277. doi: 10.3934/mbe.2017065 
[8] 
Vladimir Kazakov. Sampling  reconstruction procedure with jitter of markov continuous processes formed by stochastic differential equations of the first order. Conference Publications, 2009, 2009 (Special) : 433441. doi: 10.3934/proc.2009.2009.433 
[9] 
Jiaqin Wei, Zhuo Jin, Hailiang Yang. Optimal dividend policy with liability constraint under a hidden Markov regimeswitching model. Journal of Industrial and Management Optimization, 2019, 15 (4) : 19651993. doi: 10.3934/jimo.2018132 
[10] 
Karoline Disser, Matthias Liero. On gradient structures for Markov chains and the passage to Wasserstein gradient flows. Networks and Heterogeneous Media, 2015, 10 (2) : 233253. doi: 10.3934/nhm.2015.10.233 
[11] 
Yinghui Dong, Kam Chuen Yuen, Guojing Wang. Pricing credit derivatives under a correlated regimeswitching hazard processes model. Journal of Industrial and Management Optimization, 2017, 13 (3) : 13951415. doi: 10.3934/jimo.2016079 
[12] 
Wael Bahsoun, Paweł Góra. SRB measures for certain Markov processes. Discrete and Continuous Dynamical Systems, 2011, 30 (1) : 1737. doi: 10.3934/dcds.2011.30.17 
[13] 
Mathias Staudigl. A limit theorem for Markov decision processes. Journal of Dynamics and Games, 2014, 1 (4) : 639659. doi: 10.3934/jdg.2014.1.639 
[14] 
Artur Stephan, Holger Stephan. Memory equations as reduced Markov processes. Discrete and Continuous Dynamical Systems, 2019, 39 (4) : 21332155. doi: 10.3934/dcds.2019089 
[15] 
Martin Heida, Alexander Mielke. Averaging of timeperiodic dissipation potentials in rateindependent processes. Discrete and Continuous Dynamical Systems  S, 2017, 10 (6) : 13031327. doi: 10.3934/dcdss.2017070 
[16] 
Zhenzhong Zhang, Enhua Zhang, Jinying Tong. Necessary and sufficient conditions for ergodicity of CIR model driven by stable processes with Markov switching. Discrete and Continuous Dynamical Systems  B, 2018, 23 (6) : 24332455. doi: 10.3934/dcdsb.2018053 
[17] 
Linyi Qian, Wei Wang, Rongming Wang. Riskminimizing portfolio selection for insurance payment processes under a Markovmodulated model. Journal of Industrial and Management Optimization, 2013, 9 (2) : 411429. doi: 10.3934/jimo.2013.9.411 
[18] 
WeiJian Bo, Guo Lin. Asymptotic spreading of time periodic competition diffusion systems. Discrete and Continuous Dynamical Systems  B, 2018, 23 (9) : 39013914. doi: 10.3934/dcdsb.2018116 
[19] 
Aniello Buonocore, Luigia Caputo, Enrica Pirozzi, Maria Francesca Carfora. Gaussdiffusion processes for modeling the dynamics of a couple of interacting neurons. Mathematical Biosciences & Engineering, 2014, 11 (2) : 189201. doi: 10.3934/mbe.2014.11.189 
[20] 
Jan Haskovec, Ioannis Markou. Asymptotic flocking in the CuckerSmale model with reactiontype delays in the nonoscillatory regime. Kinetic and Related Models, 2020, 13 (4) : 795813. doi: 10.3934/krm.2020027 
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