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Periodically forced piecewise-linear adaptive exponential integrate-and-fire neuron. (English) Zbl 1277.34060

Summary: Although variability is a ubiquitous characteristic of the nervous system, under appropriate conditions neurons can generate precisely timed action potentials. Thus considerable attention has been given to the study of a neuron’s output in relation to its stimulus. In this study, we consider an increasingly popular spiking neuron model, the adaptive exponential integrate-and-fire neuron. For analytical tractability, we consider its piecewise-linear variant in order to understand the responses of such neurons to periodic stimuli. There exist regions in parameter space in which the neuron is mode locked to the periodic stimulus, and instabilities of the mode locked states lead to an Arnol’d tongue structure in parameter space. We analyze mode locked solutions and examine the bifurcations that define the boundaries of the tongue structures. The theoretical analysis is in excellent agreement with numerical simulations, and this study can be used to further understand the functional features related to responses of such a model neuron to biologically realistic inputs.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
92C20 Neural biology
34A36 Discontinuous ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
70K40 Forced motions for nonlinear problems in mechanics
34C25 Periodic solutions to ordinary differential equations
70K50 Bifurcations and instability for nonlinear problems in mechanics
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[1] DOI: 10.1103/PhysRevE.80.051922 · doi:10.1103/PhysRevE.80.051922
[2] DOI: 10.1152/jn.00686.2005 · doi:10.1152/jn.00686.2005
[3] DOI: 10.1007/s00422-011-0435-9 · Zbl 06009770 · doi:10.1007/s00422-011-0435-9
[4] DOI: 10.1016/j.physd.2003.12.009 · Zbl 1057.92016 · doi:10.1016/j.physd.2003.12.009
[5] DOI: 10.1016/j.neucom.2006.10.047 · doi:10.1016/j.neucom.2006.10.047
[6] DOI: 10.1016/S0375-9601(99)00172-3 · doi:10.1016/S0375-9601(99)00172-3
[7] DOI: 10.1103/PhysRevE.60.2086 · doi:10.1103/PhysRevE.60.2086
[8] DOI: 10.1103/PhysRevE.64.041914 · doi:10.1103/PhysRevE.64.041914
[9] DOI: 10.1016/j.physd.2011.05.012 · doi:10.1016/j.physd.2011.05.012
[10] DOI: 10.1007/s10827-009-0164-4 · Zbl 05784974 · doi:10.1007/s10827-009-0164-4
[11] DOI: 10.1162/08997660152002861 · Zbl 0963.68647 · doi:10.1162/08997660152002861
[12] DOI: 10.4249/scholarpedia.8427 · doi:10.4249/scholarpedia.8427
[13] DOI: 10.1162/neco.2007.19.3.706 · Zbl 1117.92006 · doi:10.1162/neco.2007.19.3.706
[14] DOI: 10.1007/s00422-008-0261-x · Zbl 1161.92009 · doi:10.1007/s00422-008-0261-x
[15] DOI: 10.1162/089976600300015277 · doi:10.1162/089976600300015277
[16] DOI: 10.1085/jgp.59.6.767 · doi:10.1085/jgp.59.6.767
[17] DOI: 10.1371/journal.pcbi.1002478 · doi:10.1371/journal.pcbi.1002478
[18] DOI: 10.1142/S0218127405012557 · Zbl 1089.37052 · doi:10.1142/S0218127405012557
[19] McCormick D., J. Neurophysiol. 68 pp 1384– (1992)
[20] DOI: 10.1016/0378-5955(83)90062-X · doi:10.1016/0378-5955(83)90062-X
[21] DOI: 10.1007/s00422-008-0264-7 · Zbl 1161.92012 · doi:10.1007/s00422-008-0264-7
[22] Smith G. D., J. Neurophysiol. 83 pp 588– (2000)
[23] DOI: 10.1142/S0218127409024347 · Zbl 1175.34063 · doi:10.1142/S0218127409024347
[24] DOI: 10.1137/S0036139901393500 · Zbl 1036.34047 · doi:10.1137/S0036139901393500
[25] DOI: 10.1007/s00422-008-0267-4 · Zbl 1161.92016 · doi:10.1007/s00422-008-0267-4
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