Research Article
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Effects of Weak Signal Frequency on Multiple Stochastic Resonance Induced by Feedback Mechanism

Year 2024, Volume: 14 Issue: 1, 80 - 91, 29.04.2024

Abstract

The mechanism of signal perception in the nervous system is highly complex and heavily dependent on environmental factors. One of the most significant factors affecting this mechanism is the naturally emerging noise at both the micro and macro levels of the brain. Experimental and numerical studies demonstrate that the nervous system utilizes noise to optimize its information processing capacity. Maximizing the weak signal capacity of neurons at a sufficient noise level is explained with the concept of “stochastic resonance”. This study examines the effects of weak signal frequency on the stochastic resonance phenomenon triggered by ion channel noise depending on the biological functions of the feedback mechanism in Hodgkin-Huxley neurons with an electrical feedback connection. The findings indicate that the autaptic feedback mechanism significantly enhances the signal coding capacity of Hodgkin-Huxley neurons across all frequencies within the range of frequencies to which the neuron is sensitive. Also, it is observed that the subthreshold signal detection capacity of Hodgkin-Huxley neurons exhibits resonance behaviour depending on feedback coupling strength at the appropriate feedback time delays for all frequencies in this range. Furthermore, it is shown that the maximal weak signal coding performance of Hodgkin-Huxley neuron displays multiple stochastic resonance phenomena depending on the feedback time delay. These points of maximal stochastic resonance are determined by the frequency of the applied weak signal.

References

  • Baysal, V., Calim, A. 2023. Stochastic resonance in a single autapse–coupled neuron. Chaos, Solitons & Fractals, 175:114059. Doi: https://doi.org/10.1016/j.chaos.2023.114059
  • Baysal, V., Saraç, Z., Yilmaz, E. 2019. Chaotic resonance in Hodgkin–Huxley neuron. Nonlinear Dynamics, 97:1275-1285. Doi: https://doi.org/10.1007/s11071-019-05047-w
  • Baysal, V., Yılmaz, E., Özer, M. 2015. Effects of autapse on the transmission of localized rhythmic activity in small-world neuronal networks. In 2015 23nd Signal Processing and Communications Applications Conference (SIU) (pp. 1110-1113). IEEE. Doi: 10.1109/SIU.2015.7130029
  • Bean, BP. 2007. The action potential in mammalian central neurons. Nature Reviews Neuroscience, 8(6):451-465. Doi: https://doi.org/10.1038/nrn2148
  • Bezrukov, SM., Vodyanoy, I. 1995. Noise-induced enhancement of signal transduction across voltage-dependent ion channels. Nature, 378(6555):362-364. Doi: 10.1038/378362a0
  • Chow, CC., White, JA. 1996. Spontaneous action potentials due to channel fluctuations. Biophysical journal, 71(6):3013-3021. Doi: 10.1016/S0006-3495(96)79494-8
  • Cobb, SR., Halasy, K., Vida, I., Nyı́ri, G., Tamás, G., Buhl, E. H., Somogyi, P. 1997. Synaptic effects of identified interneurons innervating both interneurons and pyramidal cells in the rat hippocampus. Neuroscience, 79(3):629-648. Doi:https://doi.org/10.1016/S0306-4522(97)00055-9
  • DiFiglia, M., Pasik, P., Pasik, T. (1976). A Golgi study of neuronal types in the neostriatum of monkeys. Brain research, 114(2):245-256. Doi: 10.1016/0006-8993(76)90669-7
  • Douglass, JK., Wilkens, L., Pantazelou, E., Moss, F. 1993. Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance. Nature, 365(6444):337-340. Doi:10.1038/365337a0
  • Faisal, AA., White, JA., Laughlin, SB. 2005. Ion-channel noise places limits on the miniaturization of the brain’s wiring. Current Biology, 15(12):1143-1149. Doi: https://doi.org/10.1016/j.cub.2005.05.056
  • Fox, RF. 1997. Stochastic versions of the Hodgkin-Huxley equations. Biophysical journal, 72(5):2068-2074. Doi: 10.1016/S0006-3495(97)78850-7
  • Guo, D., Wu, S., Chen, M., Perc, M., Zhang, Y., Ma, J., Yao, D. 2016. Regulation of irregular neuronal firing by autaptic transmission. Scientific reports, 6(1):26096. Doi: https://doi.org/10.1038/srep26096
  • Hamill, OP., Marty, A., Neher, E., Sakmann, B., Sigworth, FJ. 1981. Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches. Pflügers Archiv, 391:85-100. Doi: 10.1007/BF00656997
  • Hodgkin, AL., Huxley, AF. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of physiology, 117(4):500. Doi: 10.1113/jphysiol.1952.sp004764
  • Jung, P., Shuai, JW. 2001. Optimal sizes of ion channel clusters. Europhysics Letters, 56(1):29. Doi: 10.1209/epl/i2001-00483-y
  • Karabelas, AB., Purrura, DP. 1980. Evidence for autapses in the substantia nigra. Brain research, 200(2):467-473. Doi: 10.1016/0006-8993(80)90935-x
  • Lecar, H., Nossal, R. 1971. Theory of threshold fluctuations in nerves: I. Relationships between electrical noise and fluctuations in axon firing. Biophysical journal, 11(12):1048-1067. Doi: 10.1016/S0006-3495(71)86277-X
  • Levin, JE., Miller, JP. 1996. Broadband neural encoding in the cricket cereal sensory system enhanced by stochastic resonance. Nature, 380(6570):165-168. Doi:https://doi.org/10.1038/380165a0
  • Lübke, J., Markram, H., Frotscher, M., Sakmann, B. 1996. Frequency and dendritic distribution of autapses established by layer 5 pyramidal neurons in the developing rat neocortex: comparison with synaptic innervation of adjacent neurons of the same class. Journal of Neuroscience, 16(10):3209-3218. Doi:10.1523/JNEUROSCI.16-10-03209.1996
  • Ma, J., Song, X., Jin, W., Wang, C. 2015. Autapse-induced synchronization in a coupled neuronal network. Chaos, Solitons & Fractals, 80:31-38. Doi:https://doi.org/10.1016/j.chaos.2015.02.005
  • Miller, R. 2007. Theory of the normal waking EEG: from single neurones to waveforms in the alpha, beta and gamma frequency ranges. International journal of psychophysiology, 64(1):18-23. Doi: https://doi.org/10.1016/j.ijpsycho.2006.07.009
  • Moss, F., Ward, LM., Sannita, WG. 2004. Stochastic resonance and sensory information processing: a tutorial and review of application. Clinical neurophysiology, 115(2):267-281. Doi:https://doi.org/10.1016/j.clinph.2003.09.014
  • Ozer, M., Ekmekci, NH. 2005. Effect of channel noise on the time-course of recovery from inactivation of sodium channels. Physics Letters A, 338(2):150-154. Doi:https://doi.org/10.1016/j.physleta.2005.02.039
  • Park, MR., Lighthall, JW., Kitai, ST. 1980. Recurrent inhibition in the rat neostriatum. Brain research, 194(2):359-369. Doi:10.1016/0006-8993(80)91217-2
  • Peters, A., Proskauer, CC. 1980. Synaptic relationships between a multipolar stellate cell and a pyramidal neuron in the rat visual cortex. A combined Golgi-electron microscope study. Journal of neurocytology, 9:163-183. Doi:10.1007/BF01205156
  • Preston, RJ., Bishop, GA., Kitai, ST. 1980. Medium spiny neuron projection from the rat striatum: an intracellular horseradish peroxidase study. Brain research, 183(2):253-263. Doi: 10.1016/0006-8993(80)90462-x
  • Rubinstein, JT. 1995. Threshold fluctuations in an N sodium channel model of the node of Ranvier. Biophysical journal, 68(3):779-785. Doi:https://doi.org/10.1016/S0006-3495(95)80252-3
  • Saada, R., Miller, N., Hurwitz, I., Susswein, AJ. 2009. Autaptic excitation elicits persistent activity and a plateau potential in a neuron of known behavioral function. Current Biology, 19(6):479-484. Doi:https://doi.org/10.1016/j.cub.2009.01.060
  • Scheibel, ME., Scheibel, AB. 1971. Inhibition and the Renshaw Cell A Structural Critique; pp. 73–93. Brain, Behavior and Evolution, 4(1):73-93. Doi:10.1159/000125424
  • Schmid, G., Goychuk, I., Hänggi, P. 2003. Channel noise and synchronization in excitable membranes. Physica A: Statistical Mechanics and its Applications, 325(1-2):165-175. Doi:https://doi.org/10.1016/S0378-4371(03)00195-X
  • Schneidman, E., Freedman, B., Segev, I. 1998. Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural computation, 10(7):1679-1703. Doi:https://doi.org/10.1162/089976698300017089
  • Shkolnik-Yarros, E. 2012. Neurons and interneuronal connections of the central visual system. Springer Science & Business Media. Doi:https://doi.org/10.1007/978-1-4684-0715-0
  • Skaugen, E., Walløe, L. 1979. Firing behaviour in a stochastic nerve membrane model based upon the Hodgkin—Huxley equations. Acta Physiologica Scandinavica, 107(4):343-363. Doi:10.1111/j.1748-1716.1979.tb06486.x
  • Tamás, G., Buhl, EH., Somogyi, P. 1997. Massive autaptic self-innervation of GABAergic neurons in cat visual cortex. Journal of Neuroscience, 17(16): 6352-6364. Doi:10.1523/JNEUROSCI.17-16-06352.1997
  • Van Der Loos, H., Glaser, EM. 1972. Autapses in neocortex cerebri: synapses between a pyramidal cell's axon and its own dendrites. Brain research, 48:355-360. Doi:10.1016/0006-8993(72)90189-8
  • Wang, H., Chen, Y. 2016. Response of autaptic Hodgkin–Huxley neuron with noise to subthreshold sinusoidal signals. Physica A: Statistical Mechanics and its Applications, 462: 321-329. Doi: https://doi.org/10.1016/j.physa.2016.06.019
  • Wang, H., Ma, J., Chen, Y., Chen, Y. 2014. Effect of an autapse on the firing pattern transition in a bursting neuron. Communications in Nonlinear Science and Numerical Simulation, 19(9):3242-3254. Doi:https://doi.org/10.1016/j.cnsns.2014.02.018
  • Yilmaz, E., Ozer, M. 2015. Delayed feedback and detection of weak periodic signals in a stochastic Hodgkin–Huxley neuron. Physica A: Statistical Mechanics and its Applications, 421:455-462. Doi: https://doi.org/10.1016/j.physa.2014.10.096
  • Yilmaz, E., Baysal, V., Perc, M., Ozer, M. 2016a. Enhancement of pacemaker induced stochastic resonance by an autapse in a scale-free neuronal network. Science China Technological Sciences, 59:364-370. Doi: https://doi.org/10.1007/s11431-015-5984-z
  • Yilmaz, E., Ozer, M., Baysal, V., Perc, M. 2016b. Autapse-induced multiple coherence resonance in single neurons and neuronal networks. Scientific Reports, 6(1):30914. Doi:https://doi.org/10.1038/srep30914

Zayıf Sinyal Frekansının Geribesleme Mekanizması Tarafından İndüklenen Çoklu Stokastik Rezonans Üzerindeki Etkileri

Year 2024, Volume: 14 Issue: 1, 80 - 91, 29.04.2024

Abstract

Sinir sisteminde sinyal algılama mekanizması oldukça karmaşıktır ve çevresel faktörlere oldukça bağımlıdır. Beynin hem mikro hem de makro seviyesinde doğal olarak bulunan gürültü, bu mekanizmayı etkileyen en önemli faktörlerden biridir. Deneysel ve sayısal çalışmalar, nöronal sistemin, bilgi işleme kapasitesini optimal şekilde kullanmak için gürültüden faydalandığını göstermektedir. Nöronların zayıf sinyal sezinleme kapasitesinin, belirli bir gürültü seviyesinde maksimize olması stokastik rezonans kavramı ile açıklanmaktadır. Bu çalışmada, zayıf sinyal frekansının, elektriksel autaptik bir bağlantıya sahip Hodgkin-Huxley nöronlarında iyon kanal gürültüsü tarafından tetiklenen stokastik rezonans olgusuna olan etkileri, autaptik bağlantının biyolojik fonksiyonlarına bağlı olarak ele alınmıştır. Elde edilen bulgular, autaptik geri besleme bağlantısının, nöronun sinyallere duyarlı olduğu frekans aralığındaki bütün frekanslarda Hodgkin-Huxley nöronlarının sinyal algılama kapasitesini önemli ölçüde geliştirdiğini göstermiştir. Ayrıca, eşik altı sinyalin bu aralıktaki bütün frekanslarında Hodgkin-Huxley öronunun sinyal algılama kapasitesinin, uygun autaptik zaman gecikme değerlerinde autaptik iletkenliğe bağlı olarak rezonans davranışı sergilediği görülmüştür. Ek olarak, zayıf sinyalin bütün frekanslarında Hodgkin-Huxley nöronunun maksimal sinyal algılama performansının, autaptik zaman gecikmesine bağlı olarak çoklu stokastik rezonans fenomeni sergilediği görülmektedir. Bu stokastik rezonansların maksimal olduğu autaptik zaman gecikmesi noktaları, uygulanan zayıf sinyal frekansı tarafından belirlenmektedir.

References

  • Baysal, V., Calim, A. 2023. Stochastic resonance in a single autapse–coupled neuron. Chaos, Solitons & Fractals, 175:114059. Doi: https://doi.org/10.1016/j.chaos.2023.114059
  • Baysal, V., Saraç, Z., Yilmaz, E. 2019. Chaotic resonance in Hodgkin–Huxley neuron. Nonlinear Dynamics, 97:1275-1285. Doi: https://doi.org/10.1007/s11071-019-05047-w
  • Baysal, V., Yılmaz, E., Özer, M. 2015. Effects of autapse on the transmission of localized rhythmic activity in small-world neuronal networks. In 2015 23nd Signal Processing and Communications Applications Conference (SIU) (pp. 1110-1113). IEEE. Doi: 10.1109/SIU.2015.7130029
  • Bean, BP. 2007. The action potential in mammalian central neurons. Nature Reviews Neuroscience, 8(6):451-465. Doi: https://doi.org/10.1038/nrn2148
  • Bezrukov, SM., Vodyanoy, I. 1995. Noise-induced enhancement of signal transduction across voltage-dependent ion channels. Nature, 378(6555):362-364. Doi: 10.1038/378362a0
  • Chow, CC., White, JA. 1996. Spontaneous action potentials due to channel fluctuations. Biophysical journal, 71(6):3013-3021. Doi: 10.1016/S0006-3495(96)79494-8
  • Cobb, SR., Halasy, K., Vida, I., Nyı́ri, G., Tamás, G., Buhl, E. H., Somogyi, P. 1997. Synaptic effects of identified interneurons innervating both interneurons and pyramidal cells in the rat hippocampus. Neuroscience, 79(3):629-648. Doi:https://doi.org/10.1016/S0306-4522(97)00055-9
  • DiFiglia, M., Pasik, P., Pasik, T. (1976). A Golgi study of neuronal types in the neostriatum of monkeys. Brain research, 114(2):245-256. Doi: 10.1016/0006-8993(76)90669-7
  • Douglass, JK., Wilkens, L., Pantazelou, E., Moss, F. 1993. Noise enhancement of information transfer in crayfish mechanoreceptors by stochastic resonance. Nature, 365(6444):337-340. Doi:10.1038/365337a0
  • Faisal, AA., White, JA., Laughlin, SB. 2005. Ion-channel noise places limits on the miniaturization of the brain’s wiring. Current Biology, 15(12):1143-1149. Doi: https://doi.org/10.1016/j.cub.2005.05.056
  • Fox, RF. 1997. Stochastic versions of the Hodgkin-Huxley equations. Biophysical journal, 72(5):2068-2074. Doi: 10.1016/S0006-3495(97)78850-7
  • Guo, D., Wu, S., Chen, M., Perc, M., Zhang, Y., Ma, J., Yao, D. 2016. Regulation of irregular neuronal firing by autaptic transmission. Scientific reports, 6(1):26096. Doi: https://doi.org/10.1038/srep26096
  • Hamill, OP., Marty, A., Neher, E., Sakmann, B., Sigworth, FJ. 1981. Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches. Pflügers Archiv, 391:85-100. Doi: 10.1007/BF00656997
  • Hodgkin, AL., Huxley, AF. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of physiology, 117(4):500. Doi: 10.1113/jphysiol.1952.sp004764
  • Jung, P., Shuai, JW. 2001. Optimal sizes of ion channel clusters. Europhysics Letters, 56(1):29. Doi: 10.1209/epl/i2001-00483-y
  • Karabelas, AB., Purrura, DP. 1980. Evidence for autapses in the substantia nigra. Brain research, 200(2):467-473. Doi: 10.1016/0006-8993(80)90935-x
  • Lecar, H., Nossal, R. 1971. Theory of threshold fluctuations in nerves: I. Relationships between electrical noise and fluctuations in axon firing. Biophysical journal, 11(12):1048-1067. Doi: 10.1016/S0006-3495(71)86277-X
  • Levin, JE., Miller, JP. 1996. Broadband neural encoding in the cricket cereal sensory system enhanced by stochastic resonance. Nature, 380(6570):165-168. Doi:https://doi.org/10.1038/380165a0
  • Lübke, J., Markram, H., Frotscher, M., Sakmann, B. 1996. Frequency and dendritic distribution of autapses established by layer 5 pyramidal neurons in the developing rat neocortex: comparison with synaptic innervation of adjacent neurons of the same class. Journal of Neuroscience, 16(10):3209-3218. Doi:10.1523/JNEUROSCI.16-10-03209.1996
  • Ma, J., Song, X., Jin, W., Wang, C. 2015. Autapse-induced synchronization in a coupled neuronal network. Chaos, Solitons & Fractals, 80:31-38. Doi:https://doi.org/10.1016/j.chaos.2015.02.005
  • Miller, R. 2007. Theory of the normal waking EEG: from single neurones to waveforms in the alpha, beta and gamma frequency ranges. International journal of psychophysiology, 64(1):18-23. Doi: https://doi.org/10.1016/j.ijpsycho.2006.07.009
  • Moss, F., Ward, LM., Sannita, WG. 2004. Stochastic resonance and sensory information processing: a tutorial and review of application. Clinical neurophysiology, 115(2):267-281. Doi:https://doi.org/10.1016/j.clinph.2003.09.014
  • Ozer, M., Ekmekci, NH. 2005. Effect of channel noise on the time-course of recovery from inactivation of sodium channels. Physics Letters A, 338(2):150-154. Doi:https://doi.org/10.1016/j.physleta.2005.02.039
  • Park, MR., Lighthall, JW., Kitai, ST. 1980. Recurrent inhibition in the rat neostriatum. Brain research, 194(2):359-369. Doi:10.1016/0006-8993(80)91217-2
  • Peters, A., Proskauer, CC. 1980. Synaptic relationships between a multipolar stellate cell and a pyramidal neuron in the rat visual cortex. A combined Golgi-electron microscope study. Journal of neurocytology, 9:163-183. Doi:10.1007/BF01205156
  • Preston, RJ., Bishop, GA., Kitai, ST. 1980. Medium spiny neuron projection from the rat striatum: an intracellular horseradish peroxidase study. Brain research, 183(2):253-263. Doi: 10.1016/0006-8993(80)90462-x
  • Rubinstein, JT. 1995. Threshold fluctuations in an N sodium channel model of the node of Ranvier. Biophysical journal, 68(3):779-785. Doi:https://doi.org/10.1016/S0006-3495(95)80252-3
  • Saada, R., Miller, N., Hurwitz, I., Susswein, AJ. 2009. Autaptic excitation elicits persistent activity and a plateau potential in a neuron of known behavioral function. Current Biology, 19(6):479-484. Doi:https://doi.org/10.1016/j.cub.2009.01.060
  • Scheibel, ME., Scheibel, AB. 1971. Inhibition and the Renshaw Cell A Structural Critique; pp. 73–93. Brain, Behavior and Evolution, 4(1):73-93. Doi:10.1159/000125424
  • Schmid, G., Goychuk, I., Hänggi, P. 2003. Channel noise and synchronization in excitable membranes. Physica A: Statistical Mechanics and its Applications, 325(1-2):165-175. Doi:https://doi.org/10.1016/S0378-4371(03)00195-X
  • Schneidman, E., Freedman, B., Segev, I. 1998. Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural computation, 10(7):1679-1703. Doi:https://doi.org/10.1162/089976698300017089
  • Shkolnik-Yarros, E. 2012. Neurons and interneuronal connections of the central visual system. Springer Science & Business Media. Doi:https://doi.org/10.1007/978-1-4684-0715-0
  • Skaugen, E., Walløe, L. 1979. Firing behaviour in a stochastic nerve membrane model based upon the Hodgkin—Huxley equations. Acta Physiologica Scandinavica, 107(4):343-363. Doi:10.1111/j.1748-1716.1979.tb06486.x
  • Tamás, G., Buhl, EH., Somogyi, P. 1997. Massive autaptic self-innervation of GABAergic neurons in cat visual cortex. Journal of Neuroscience, 17(16): 6352-6364. Doi:10.1523/JNEUROSCI.17-16-06352.1997
  • Van Der Loos, H., Glaser, EM. 1972. Autapses in neocortex cerebri: synapses between a pyramidal cell's axon and its own dendrites. Brain research, 48:355-360. Doi:10.1016/0006-8993(72)90189-8
  • Wang, H., Chen, Y. 2016. Response of autaptic Hodgkin–Huxley neuron with noise to subthreshold sinusoidal signals. Physica A: Statistical Mechanics and its Applications, 462: 321-329. Doi: https://doi.org/10.1016/j.physa.2016.06.019
  • Wang, H., Ma, J., Chen, Y., Chen, Y. 2014. Effect of an autapse on the firing pattern transition in a bursting neuron. Communications in Nonlinear Science and Numerical Simulation, 19(9):3242-3254. Doi:https://doi.org/10.1016/j.cnsns.2014.02.018
  • Yilmaz, E., Ozer, M. 2015. Delayed feedback and detection of weak periodic signals in a stochastic Hodgkin–Huxley neuron. Physica A: Statistical Mechanics and its Applications, 421:455-462. Doi: https://doi.org/10.1016/j.physa.2014.10.096
  • Yilmaz, E., Baysal, V., Perc, M., Ozer, M. 2016a. Enhancement of pacemaker induced stochastic resonance by an autapse in a scale-free neuronal network. Science China Technological Sciences, 59:364-370. Doi: https://doi.org/10.1007/s11431-015-5984-z
  • Yilmaz, E., Ozer, M., Baysal, V., Perc, M. 2016b. Autapse-induced multiple coherence resonance in single neurons and neuronal networks. Scientific Reports, 6(1):30914. Doi:https://doi.org/10.1038/srep30914
There are 40 citations in total.

Details

Primary Language Turkish
Subjects Neural Engineering
Journal Section Research Articles
Authors

Veli Baysal 0000-0001-6504-1653

Publication Date April 29, 2024
Submission Date February 18, 2024
Acceptance Date March 19, 2024
Published in Issue Year 2024 Volume: 14 Issue: 1

Cite

APA Baysal, V. (2024). Zayıf Sinyal Frekansının Geribesleme Mekanizması Tarafından İndüklenen Çoklu Stokastik Rezonans Üzerindeki Etkileri. Karaelmas Fen Ve Mühendislik Dergisi, 14(1), 80-91.
AMA Baysal V. Zayıf Sinyal Frekansının Geribesleme Mekanizması Tarafından İndüklenen Çoklu Stokastik Rezonans Üzerindeki Etkileri. Karaelmas Fen ve Mühendislik Dergisi. April 2024;14(1):80-91.
Chicago Baysal, Veli. “Zayıf Sinyal Frekansının Geribesleme Mekanizması Tarafından İndüklenen Çoklu Stokastik Rezonans Üzerindeki Etkileri”. Karaelmas Fen Ve Mühendislik Dergisi 14, no. 1 (April 2024): 80-91.
EndNote Baysal V (April 1, 2024) Zayıf Sinyal Frekansının Geribesleme Mekanizması Tarafından İndüklenen Çoklu Stokastik Rezonans Üzerindeki Etkileri. Karaelmas Fen ve Mühendislik Dergisi 14 1 80–91.
IEEE V. Baysal, “Zayıf Sinyal Frekansının Geribesleme Mekanizması Tarafından İndüklenen Çoklu Stokastik Rezonans Üzerindeki Etkileri”, Karaelmas Fen ve Mühendislik Dergisi, vol. 14, no. 1, pp. 80–91, 2024.
ISNAD Baysal, Veli. “Zayıf Sinyal Frekansının Geribesleme Mekanizması Tarafından İndüklenen Çoklu Stokastik Rezonans Üzerindeki Etkileri”. Karaelmas Fen ve Mühendislik Dergisi 14/1 (April 2024), 80-91.
JAMA Baysal V. Zayıf Sinyal Frekansının Geribesleme Mekanizması Tarafından İndüklenen Çoklu Stokastik Rezonans Üzerindeki Etkileri. Karaelmas Fen ve Mühendislik Dergisi. 2024;14:80–91.
MLA Baysal, Veli. “Zayıf Sinyal Frekansının Geribesleme Mekanizması Tarafından İndüklenen Çoklu Stokastik Rezonans Üzerindeki Etkileri”. Karaelmas Fen Ve Mühendislik Dergisi, vol. 14, no. 1, 2024, pp. 80-91.
Vancouver Baysal V. Zayıf Sinyal Frekansının Geribesleme Mekanizması Tarafından İndüklenen Çoklu Stokastik Rezonans Üzerindeki Etkileri. Karaelmas Fen ve Mühendislik Dergisi. 2024;14(1):80-91.