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Rotation-controlled Wilson-Cowan neuron model and its hardware

Year 2022, Volume: 11 Issue: 1, 77 - 83, 14.01.2022
https://doi.org/10.28948/ngumuh.1002174

Abstract

Various biological neuron models have been defined by using nonlinear function definitions in order to explain the characteristic dynamics of neurons that are the basic elements of the communication network in the living body. In the analysis of these models, the solution methods used in the analysis of nonlinear systems are frequently used. In recent years, some of the studies about nonlinear systems have been encountered with the rotational attractor structures. In this study, it is aimed to provide phase control of the rotational attractor obtained by applying the Euler Rotation Theorem to the Wilson Cowan (W-C) neuron model that is used effectively in the literature to define excitatory and inhibitory synapse structures. In addition, the FPGA (Field Programmable Gate Array)-based hardware implementation study of the rotation-controlled W-C neuron model have also been carried out in order to see its usability in studies required to the real-time signals. With the numerical analyzes, it has been seen that the attractor structure of the rotation-controlled W-C neuron model can be controlled successfully. On the other hand, an alternative study has been reported for the systems designed by inspiring the biology and emulated with electronic equipment.

References

  • E. R. Kandel, J. H. Schwartz ve T. M. Jessell, Principles of Neural Science. 4th ed. McGraw-Hill, New York. ISBN 0- 8385-7701-6, 2000.
  • A. L. Hodgkin ve A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nevre. The Journal of Physiology, 117(4), 500-544, 1952. https://doi.org/ 10.1113/ jphysiol .1952 .sp004764
  • R. FitzHugh, Mathematical models for excitation and propagation in nerve. In: Schawn, H.P. (ed.) Biological Engineering, vol. 1, pp. 1–85. McGraw-Hill, New York, 1969.
  • J. L. Hindmarsh ve R. M. Rose, A model of neural bursting using three couple first order differential equations. Proceedings of the Royal Society B: Biological Sciences, 221(1222), 87–102, 1984. https://doi.org/10.1098/rspb.1984.0024
  • E. M. Izhikevich, Simple model of spiking neurons. IEEE Transactions on Neural Networks and Learning Systems, 14(6), 1569–1572, 2003. https://doi.org/ 10.1109/tnn.2003.820440
  • H. R. Wilson ve J. D. Cowan, Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12 (1), 1–24, 1972. https://doi.org/10.1016/ S0006-3495(72)86068-5
  • M. Bertalmío ve J. D Cowan, Implementing the Retinex algorithm with Wilson–Cowan equations. Journal of Physiology - Paris, 103(1-2), 69-72, 2009. https://doi.org/ 10.1016/j.jphysparis.2009.05.001
  • X. Lin, S. Zhou, Li, H. Tang ve Y. Qi, Rhythm oscillation in fractional order Relaxation oscillator and its application in image enhancement. Journal of Computational and Applied Mathematics, 339, 69-84, 2018. https://doi.org/10.1016/ j.cam.2018.01.027
  • C. M. Pinto ve A. P. Santos, Modelling gait transition in two-legged animals. Communications in Nonlinear Science and Numerical Simulation, 16(12), 4625- 4631, 2011. https://doi.org/10.1016/j.cnsns.2011. 05.033
  • L. M. Pecora ve T. L. Carroll, Synchronization in chaotic systems. Physical Review Letters, 64(8), 821, 1990. https://doi.org/10.1063/1.4917383
  • S. K. Bhowmick, B. K. Bera ve D. Ghosh, Generalized counter-rotating oscillators: mixed synchronization. Communications in Nonlinear Science and Numerical Simulation, 22(1–3), 692–701, 2015. https://doi.org/ 10.1016/j.cnsns.2014.09.024
  • A. Sharma, M. Dev Shrimali ve S. Kumar Dana, Phase-flip transition in nonlinear oscillators coupled by dynamic environment. Chaos, 22(2), 023147, 2012. https://doi.org/10.1063/1.4729459
  • A. Prasad, S. K. Dana, R. Karnatak, J. Kurths, B. Blasius ve R. Ramaswamy, Universal occurrence of the phase-flip bifurcation in time-delay coupled systems. Chaos, 18(2), 023111, 2008. https://doi.org/10.1063/ 1.2905146
  • G. B. Arfken, H. J. Weber, Mathematical methods for physicists. 6th edn. Elsevier Academic Press, Cambridge. ISBN 0-12-088584-0, 1999.
  • N. Korkmaz, A Phase Control Method for the Dynamical Attractor of the HR Neuron Model: The Rotation-Transition Process and Its Experimental Realization. Neural Processing Letters, 53, 3877–3892, 2021. https://doi.org/10 .1007/s11063-021-10568-w
  • H. R. Wilson ve J. D Cowan, A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue, Kybernetik, 13(2), 55–80, 1973. https://doi.org/10.1007/BF00288786
  • H. R. Wilson, Spikes, decisions, and actions: the dynamical foundations of neuroscience, Oxford University Press, 1999.
  • E. Negahbani, D. A. Steyn-Ross, M. L. Steyn-Ross, M. T. Wilson ve J. W. Sleigh, Noise-induced precursors of state transitions in the stochastic Wilson–Cowan model. The Journal of Mathematical Neuroscience (JMN), 5(1), 1-27, 2015. https://doi.org/10.1186/ s13408-015-0021-x
  • S. Ahmadizadeh, D. Nešić, D. R. Freestone ve D. B. Grayden, On synchronization of networks of Wilson–Cowan oscillators with diffusive coupling. Automatica, 71, 169-178, 2016. https://doi.org/10.1016 /j.automati ca .2016.04.030
  • J. D. Cowan, J. Neuman ve W. Van Drongelen, Wilson–Cowan equations for neocortical Dynamics. The Journal of Mathematical Neuroscience, 6(1), 1-24, 2016. https://doi.org/10.1186/s13408-015-0034-5
  • P. J. Srinidhi, T. R. Yashaswini, N. Uttunga, S. A Ali ve M. R. Ahmed, Implementation of STDP based learning rule in neuromorphic CMOS circuits. In IEEE 2017 International Conference on Intelligent Computing and Control Systems (ICICCS), 1105-1110, Madurai, India, June 2017. doi: 10.1109/ıccons.2017.8250637
  • www.xilinx.com, Date of access: 28.09.2021.

Rotasyon kontrollü Wilson-Cowan nöron modeli ve donanım gerçekleştirimi

Year 2022, Volume: 11 Issue: 1, 77 - 83, 14.01.2022
https://doi.org/10.28948/ngumuh.1002174

Abstract

Canlı vücudundaki iletişim ağının temel elemanı olan nöronların karakteristik dinamiklerini açıklamak için, doğrusal olmayan fonksiyon tanımlamalarından yararlanılarak çeşitli biyolojik nöron modelleri tanımlanmıştır. Bu modellerin analizlerinde, doğrusal olmayan sistemlerin analizlerinde kullanılan çözüm yöntemlerinden sıklıkla yararlanılmaktadır. Son yıllarda doğrusal olmayan sistemleri konu alan çalışmaların bir kısmında rotasyonlu çeker yapıları ile karşılaşılmaktadır. Bu çalışmada, literatürde uyarıcı ve engelleyici sinaps yapılarını tanımlamada etkin kullanılan Wilson Cowan (W-C) nöron modeline Euler Rotasyon Teoremi’nin uygulanması ile elde edilen rotasyonlu çekerin faz kontrolünün sağlanması amaçlanmıştır. Ayrıca, gerçek zamanlı işaretlere ihtiyaç duyulabilecek çalışmalarda kullanılabilirliğinin gösterilmesi amacı ile rotasyon kontrollü W-C nöron modelinin FPGA (Field Programmable Gate Array) tabanlı donanım gerçekleştirim çalışması da yapılmıştır. Yapılan nümerik analizler ile rotasyon kontrollü W-C nöron modelinin çeker yapısının başarılı bir şekilde kontrol edilebildiği görülmüştür. Öte yandan deneysel gerçekleştirim çalışmaları ile biyolojiden esinlenilerek tasarlanan ve elektronik ekipmanlarla taklit edilen sistemler için alternatif bir çalışma kaydedilmiştir.

References

  • E. R. Kandel, J. H. Schwartz ve T. M. Jessell, Principles of Neural Science. 4th ed. McGraw-Hill, New York. ISBN 0- 8385-7701-6, 2000.
  • A. L. Hodgkin ve A. F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nevre. The Journal of Physiology, 117(4), 500-544, 1952. https://doi.org/ 10.1113/ jphysiol .1952 .sp004764
  • R. FitzHugh, Mathematical models for excitation and propagation in nerve. In: Schawn, H.P. (ed.) Biological Engineering, vol. 1, pp. 1–85. McGraw-Hill, New York, 1969.
  • J. L. Hindmarsh ve R. M. Rose, A model of neural bursting using three couple first order differential equations. Proceedings of the Royal Society B: Biological Sciences, 221(1222), 87–102, 1984. https://doi.org/10.1098/rspb.1984.0024
  • E. M. Izhikevich, Simple model of spiking neurons. IEEE Transactions on Neural Networks and Learning Systems, 14(6), 1569–1572, 2003. https://doi.org/ 10.1109/tnn.2003.820440
  • H. R. Wilson ve J. D. Cowan, Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal, 12 (1), 1–24, 1972. https://doi.org/10.1016/ S0006-3495(72)86068-5
  • M. Bertalmío ve J. D Cowan, Implementing the Retinex algorithm with Wilson–Cowan equations. Journal of Physiology - Paris, 103(1-2), 69-72, 2009. https://doi.org/ 10.1016/j.jphysparis.2009.05.001
  • X. Lin, S. Zhou, Li, H. Tang ve Y. Qi, Rhythm oscillation in fractional order Relaxation oscillator and its application in image enhancement. Journal of Computational and Applied Mathematics, 339, 69-84, 2018. https://doi.org/10.1016/ j.cam.2018.01.027
  • C. M. Pinto ve A. P. Santos, Modelling gait transition in two-legged animals. Communications in Nonlinear Science and Numerical Simulation, 16(12), 4625- 4631, 2011. https://doi.org/10.1016/j.cnsns.2011. 05.033
  • L. M. Pecora ve T. L. Carroll, Synchronization in chaotic systems. Physical Review Letters, 64(8), 821, 1990. https://doi.org/10.1063/1.4917383
  • S. K. Bhowmick, B. K. Bera ve D. Ghosh, Generalized counter-rotating oscillators: mixed synchronization. Communications in Nonlinear Science and Numerical Simulation, 22(1–3), 692–701, 2015. https://doi.org/ 10.1016/j.cnsns.2014.09.024
  • A. Sharma, M. Dev Shrimali ve S. Kumar Dana, Phase-flip transition in nonlinear oscillators coupled by dynamic environment. Chaos, 22(2), 023147, 2012. https://doi.org/10.1063/1.4729459
  • A. Prasad, S. K. Dana, R. Karnatak, J. Kurths, B. Blasius ve R. Ramaswamy, Universal occurrence of the phase-flip bifurcation in time-delay coupled systems. Chaos, 18(2), 023111, 2008. https://doi.org/10.1063/ 1.2905146
  • G. B. Arfken, H. J. Weber, Mathematical methods for physicists. 6th edn. Elsevier Academic Press, Cambridge. ISBN 0-12-088584-0, 1999.
  • N. Korkmaz, A Phase Control Method for the Dynamical Attractor of the HR Neuron Model: The Rotation-Transition Process and Its Experimental Realization. Neural Processing Letters, 53, 3877–3892, 2021. https://doi.org/10 .1007/s11063-021-10568-w
  • H. R. Wilson ve J. D Cowan, A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue, Kybernetik, 13(2), 55–80, 1973. https://doi.org/10.1007/BF00288786
  • H. R. Wilson, Spikes, decisions, and actions: the dynamical foundations of neuroscience, Oxford University Press, 1999.
  • E. Negahbani, D. A. Steyn-Ross, M. L. Steyn-Ross, M. T. Wilson ve J. W. Sleigh, Noise-induced precursors of state transitions in the stochastic Wilson–Cowan model. The Journal of Mathematical Neuroscience (JMN), 5(1), 1-27, 2015. https://doi.org/10.1186/ s13408-015-0021-x
  • S. Ahmadizadeh, D. Nešić, D. R. Freestone ve D. B. Grayden, On synchronization of networks of Wilson–Cowan oscillators with diffusive coupling. Automatica, 71, 169-178, 2016. https://doi.org/10.1016 /j.automati ca .2016.04.030
  • J. D. Cowan, J. Neuman ve W. Van Drongelen, Wilson–Cowan equations for neocortical Dynamics. The Journal of Mathematical Neuroscience, 6(1), 1-24, 2016. https://doi.org/10.1186/s13408-015-0034-5
  • P. J. Srinidhi, T. R. Yashaswini, N. Uttunga, S. A Ali ve M. R. Ahmed, Implementation of STDP based learning rule in neuromorphic CMOS circuits. In IEEE 2017 International Conference on Intelligent Computing and Control Systems (ICICCS), 1105-1110, Madurai, India, June 2017. doi: 10.1109/ıccons.2017.8250637
  • www.xilinx.com, Date of access: 28.09.2021.
There are 22 citations in total.

Details

Primary Language Turkish
Subjects Electrical Engineering
Journal Section Electrical and Electronics Engineering
Authors

Nimet Korkmaz 0000-0002-7419-1538

Publication Date January 14, 2022
Submission Date September 29, 2021
Acceptance Date December 14, 2021
Published in Issue Year 2022 Volume: 11 Issue: 1

Cite

APA Korkmaz, N. (2022). Rotasyon kontrollü Wilson-Cowan nöron modeli ve donanım gerçekleştirimi. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 11(1), 77-83. https://doi.org/10.28948/ngumuh.1002174
AMA Korkmaz N. Rotasyon kontrollü Wilson-Cowan nöron modeli ve donanım gerçekleştirimi. NOHU J. Eng. Sci. January 2022;11(1):77-83. doi:10.28948/ngumuh.1002174
Chicago Korkmaz, Nimet. “Rotasyon Kontrollü Wilson-Cowan nöron Modeli Ve donanım gerçekleştirimi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 11, no. 1 (January 2022): 77-83. https://doi.org/10.28948/ngumuh.1002174.
EndNote Korkmaz N (January 1, 2022) Rotasyon kontrollü Wilson-Cowan nöron modeli ve donanım gerçekleştirimi. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 11 1 77–83.
IEEE N. Korkmaz, “Rotasyon kontrollü Wilson-Cowan nöron modeli ve donanım gerçekleştirimi”, NOHU J. Eng. Sci., vol. 11, no. 1, pp. 77–83, 2022, doi: 10.28948/ngumuh.1002174.
ISNAD Korkmaz, Nimet. “Rotasyon Kontrollü Wilson-Cowan nöron Modeli Ve donanım gerçekleştirimi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 11/1 (January 2022), 77-83. https://doi.org/10.28948/ngumuh.1002174.
JAMA Korkmaz N. Rotasyon kontrollü Wilson-Cowan nöron modeli ve donanım gerçekleştirimi. NOHU J. Eng. Sci. 2022;11:77–83.
MLA Korkmaz, Nimet. “Rotasyon Kontrollü Wilson-Cowan nöron Modeli Ve donanım gerçekleştirimi”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, vol. 11, no. 1, 2022, pp. 77-83, doi:10.28948/ngumuh.1002174.
Vancouver Korkmaz N. Rotasyon kontrollü Wilson-Cowan nöron modeli ve donanım gerçekleştirimi. NOHU J. Eng. Sci. 2022;11(1):77-83.

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