Traveling pulses in a stochastic neural field model of direction selectivity
We analyze the effects of extrinsic noise on traveling pulses in a neural field model of direction selectivity. The model consists of a one-dimensional scalar neural field with an asymmetric weight distribution consisting of an offset Mexican hat function. We first show how, in the absence of any no...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2012-10-01
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| Series: | Frontiers in Computational Neuroscience |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fncom.2012.00090/full |
| _version_ | 1819052869018451968 |
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| author | Paul C Bressloff Jeremy eWilkerson |
| author_facet | Paul C Bressloff Jeremy eWilkerson |
| author_sort | Paul C Bressloff |
| collection | DOAJ |
| description | We analyze the effects of extrinsic noise on traveling pulses in a neural field model of direction selectivity. The model consists of a one-dimensional scalar neural field with an asymmetric weight distribution consisting of an offset Mexican hat function. We first show how, in the absence of any noise, the system supports spontaneously propagating traveling pulses that can lock to externally moving stimuli. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how extrinsic noise in the activity variables leads to a diffusive-like displacement (wandering) of the wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. In the case of freely propagating pulses, the wandering is characterized by pure Brownian motion, whereas in the case of stimulus-locked pulses, it is given by an Ornstein-Uhlenbeck process. This establishes that stimulus-locked pulses are more robust to noise. |
| first_indexed | 2024-12-21T12:26:41Z |
| format | Article |
| id | doaj.art-be484fdd86084dc28e5cea345a2ed709 |
| institution | Directory Open Access Journal |
| issn | 1662-5188 |
| language | English |
| last_indexed | 2024-12-21T12:26:41Z |
| publishDate | 2012-10-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Computational Neuroscience |
| spelling | doaj.art-be484fdd86084dc28e5cea345a2ed7092022-12-21T19:04:10ZengFrontiers Media S.A.Frontiers in Computational Neuroscience1662-51882012-10-01610.3389/fncom.2012.0009037078Traveling pulses in a stochastic neural field model of direction selectivityPaul C Bressloff0Jeremy eWilkerson1University of UtahUniversity of UtahWe analyze the effects of extrinsic noise on traveling pulses in a neural field model of direction selectivity. The model consists of a one-dimensional scalar neural field with an asymmetric weight distribution consisting of an offset Mexican hat function. We first show how, in the absence of any noise, the system supports spontaneously propagating traveling pulses that can lock to externally moving stimuli. Using a separation of time scales and perturbation methods previously developed for stochastic reaction-diffusion equations, we then show how extrinsic noise in the activity variables leads to a diffusive-like displacement (wandering) of the wave from its uniformly translating position at long time scales, and fluctuations in the wave profile around its instantaneous position at short time scales. In the case of freely propagating pulses, the wandering is characterized by pure Brownian motion, whereas in the case of stimulus-locked pulses, it is given by an Ornstein-Uhlenbeck process. This establishes that stimulus-locked pulses are more robust to noise.http://journal.frontiersin.org/Journal/10.3389/fncom.2012.00090/fulltraveling wavesstochastic processesDirection Selectivityneural field theorystimulus-driven |
| spellingShingle | Paul C Bressloff Jeremy eWilkerson Traveling pulses in a stochastic neural field model of direction selectivity Frontiers in Computational Neuroscience traveling waves stochastic processes Direction Selectivity neural field theory stimulus-driven |
| title | Traveling pulses in a stochastic neural field model of direction selectivity |
| title_full | Traveling pulses in a stochastic neural field model of direction selectivity |
| title_fullStr | Traveling pulses in a stochastic neural field model of direction selectivity |
| title_full_unstemmed | Traveling pulses in a stochastic neural field model of direction selectivity |
| title_short | Traveling pulses in a stochastic neural field model of direction selectivity |
| title_sort | traveling pulses in a stochastic neural field model of direction selectivity |
| topic | traveling waves stochastic processes Direction Selectivity neural field theory stimulus-driven |
| url | http://journal.frontiersin.org/Journal/10.3389/fncom.2012.00090/full |
| work_keys_str_mv | AT paulcbressloff travelingpulsesinastochasticneuralfieldmodelofdirectionselectivity AT jeremyewilkerson travelingpulsesinastochasticneuralfieldmodelofdirectionselectivity |