Research Article
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Year 2024, Volume: 2 Issue: 1, 36 - 47, 02.08.2024

Abstract

References

  • E. D. Adrian, The impulses produced by sensory nerve endings, The Journal of Physiology 61 (1) (1926) 49–72.
  • A. P. Georgopoulos, A. B. Schwartz, R. E. Kettner, Neuronal population coding of movement direction, Science 233 (4771) (1986) 1416–1419.
  • M. Abeles, Corticonics: Neural Circuits of the Cerebral Cortex, Cambridge University Press, 1991. M. Abeles, H. Bergman, E. Margalit, E. Vaadia, Spatiotemporal firing patterns in the frontal cortex of behaving monkeys, Journal of Neurophysiology 70 (4) (1993) 1629–1638.
  • W. S. McCulloch, W. Pitts, A logical calculus of the ideas immanent in nervous activity, The Bulletin of Mathematical Biophysics 5 (4) (1943) 115–133.
  • R. H. Adrian, W. K. Chandler, A. L. Hodgkin, Voltage clamp experiments in striated muscle fibres, The Journal of Physiology 208 (3) (1970) 607–644.
  • J. L. Hindmarsh, R. M. Rose, A. F. Huxley, A model of neuronal bursting using three coupled first order differential equations, Proceedings of the Royal Society of London. Series B. Biological Sciences 221 (1222) (1984) 87–102.
  • E. Izhikevich, Simple model of spiking neurons, IEEE Transactions on Neural Networks 14 (6) (2003) 1569–1572.
  • M. J. Chacron, A. Longtin, K. Pakdaman, Chaotic firing in the sinusoidally forced leaky integrate-and-fire model with threshold fatigue, Physica D: Nonlinear Phenomena 192 (1) (2004) 138–160.
  • H. Hayashi, S. Ishizuka, M. Ohta, K. Hirakawa, Chaotic behavior in the onchidium giant neuron under sinusoidal stimulation, Physics Letters A 88 (8) (1982) 435–438.
  • Y. Manor, J. Gonczarowski, I. Segev, Propagation of action potentials along complex axonal trees. model and implemen- tation, Biophysical journal 60 (6) (1991) 1411–1423.
  • L. Gammaitoni, P. Ha¨nggi, P. Jung, F. Marchesoni, Stochastic resonance, Reviews of modern physics 70 (1) (1998) 223.
  • D. F. Russell, L. A. Wilkens, F. Moss, Use of behavioural stochastic resonance by paddle fish for feeding, Nature 402 (6759) (1999) 291–294.
  • J. K. Douglass, L. Wilkens, E. Pantazelou, F. Moss, Noise enhancement of information transfer in crayfish mechanore- ceptors by stochastic resonance, Nature 365 (6444) (1993) 337–340.
  • S. Lu, Q. He, J. Wang, A review of stochastic resonance in rotating machine fault detection, Mechanical Systems and Signal Processing 116 (2019) 230–260.
  • B. McNamara, K. Wiesenfeld, Theory of stochastic resonance, Physical review A 39 (9) (1989) 4854.
  • A. Palonpon, J. Amistoso, J. Holdsworth, W. Garcia, C. Saloma, Measurement of weak transmittances by stochastic resonance, Optics letters 23 (18) (1998) 1480–1482.
  • E. Yilmaz, M. Uzuntarla, M. Ozer, M. Perc, Stochastic resonance in hybrid scale-free neuronal networks, Physica A: Statistical Mechanics and its Applications 392 (22) (2013) 5735–5741.
  • B. S. Gutkin, J. Jost, H. C. Tuckwell, Inhibition of rhythmic neural spiking by noise: the occurrence of a minimum in activity with increasing noise, Naturwissenschaften 96 (2009) 1091–1097.
  • D. Guo, Inhibition of rhythmic spiking by colored noise in neural systems, Cognitive neurodynamics 5 (2011) 293–300.
  • H. C. Tuckwell, J. Jost, The effects of various spatial distributions of weak noise on rhythmic spiking, Journal of Com- putational Neuroscience 30 (2011) 361–371.
  • D. Yu, Y. Wu, Z. Ye, F. Xiao, Y. Jia, Inverse chaotic resonance in hodgkin–huxley neuronal system, The European Physical Journal Special Topics 231 (22) (2022) 4097–4107.
  • H. Van Der Loos, E. M. Glaser, Autapses in neocortex cerebri: synapses between a pyramidal cell’s axon and its own dendrites, Brain research 48 (1972) 355–360.
  • M. R. Park, J. W. Lighthall, S. T. Kitai, Recurrent inhibition in the rat neostriatum, Brain research 194 (2) (1980) 359–369.
  • R. Preston, G. Bishop, S. Kitai, Medium spiny neuron projection from the rat striatum: an intracellular horseradish peroxidase study, Brain research 183 (2) (1980) 253–263.
  • A. B. Karabelas, D. P. Purrura, Evidence for autapses in the substantia nigra, Brain research 200 (2) (1980) 467–473.
  • R. Saada, N. Miller, I. Hurwitz, A. J. Susswein, Autaptic excitation elicits persistent activity and a plateau potential in a neuron of known behavioral function, Current Biology 19 (6) (2009) 479–484.
  • G. C. Sethia, J. Kurths, A. Sen, Coherence resonance in an excitable system with time delay, Physics Letters A 364 (3-4) (2007) 227–230. V. Baysal, E. Yılmaz, M. O¨ zer, Blocking of weak signal propagation via autaptic transmission in scale-free networks, IU-Journal of Electrical & Electronics Engineering 17 (1) (2017) 3091–3096.
  • Y. Li, G. Schmid, P. Ha¨nggi, L. Schimansky-Geier, Spontaneous spiking in an autaptic hodgkin-huxley setup, Physical Review E 82 (6) (2010) 061907.
  • H. Qin, J. Ma, C. Wang, R. Chu, Autapse-induced target wave, spiral wave in regular network of neurons, Science China Physics, Mechanics & Astronomy 57 (2014) 1918–1926.
  • H. Wang, J. Ma, Y. Chen, Y. Chen, Effect of an autapse on the firing pattern transition in a bursting neuron, Communi- cations in Nonlinear Science and Numerical Simulation 19 (9) (2014) 3242–3254.
  • E. Yilmaz, V. Baysal, M. Ozer, M. Perc, Autaptic pacemaker mediated propagation of weak rhythmic activity across small-world neuronal networks, Physica A: Statistical Mechanics and its Applications 444 (2016) 538–546.
  • C. Morris, H. Lecar, Voltage oscillations in the barnacle giant muscle fiber, Biophysical journal 35 (1) (1981) 193–213.
  • M. Uzuntarla, Inverse stochastic resonance induced by synaptic background activity with unreliable synapses, Physics Letters A 377 (38) (2013) 2585–2589.
  • E. Yilmaz, M. Ozer, Delayed feedback and detection of weak periodic signals in a stochastic hodgkin–huxley neuron, Physica A: Statistical Mechanics and its Applications 421 (2015) 455–462.
  • V. Baysal, Z. Sarac¸, E. Yilmaz, Chaotic resonance in hodgkin–huxley neuron, Nonlinear Dynamics 97 (2019) 1275– 1285.
  • W. Maass, Networks of spiking neurons: the third generation of neural network models, Neural networks 10 (9) (1997) 1659–1671.
  • D. Zhao, Y. Zeng, Y. Li, Backeisnn: A deep spiking neural network with adaptive self-feedback and balanced excitatory– inhibitory neurons, Neural Networks 154 (2022) 68–77.

EFFECTS OF CHEMICAL AUTAPSE ON INVERSE CHAOTIC RESONANCE IN MORRIS-LECAR NEURON MODEL

Year 2024, Volume: 2 Issue: 1, 36 - 47, 02.08.2024

Abstract

Inverse chaotic resonance is a phenomenon, in which the mean firing rate of a neuron exhibits a minimum depending on the chaotic signal intensity, which emerges in the firing dynamics of neurons. In this study, we have investigated the effects of inhibitory and excitatory autapses on the inverse chaotic resonance phenomenon in Morris-Lecar neurons. We show that, for proper constant stimulus current, the ML neurons exhibits inverse chaotic resonance phenomenon in the firingdynamics as a function of the intensity of the chaotic activity. In addition, we find that, at low and medium chaotic activity levels, the ML neuron shows multiple-inverse chaotic resonance phenomenon depending on autaptic time delay for low and intermediate autaptic conductances. Finally, we show that, both excitatory and inhibitory autapse augment the firing rate of the ML neuron, this increase is more in the case of excitatory autapse.

References

  • E. D. Adrian, The impulses produced by sensory nerve endings, The Journal of Physiology 61 (1) (1926) 49–72.
  • A. P. Georgopoulos, A. B. Schwartz, R. E. Kettner, Neuronal population coding of movement direction, Science 233 (4771) (1986) 1416–1419.
  • M. Abeles, Corticonics: Neural Circuits of the Cerebral Cortex, Cambridge University Press, 1991. M. Abeles, H. Bergman, E. Margalit, E. Vaadia, Spatiotemporal firing patterns in the frontal cortex of behaving monkeys, Journal of Neurophysiology 70 (4) (1993) 1629–1638.
  • W. S. McCulloch, W. Pitts, A logical calculus of the ideas immanent in nervous activity, The Bulletin of Mathematical Biophysics 5 (4) (1943) 115–133.
  • R. H. Adrian, W. K. Chandler, A. L. Hodgkin, Voltage clamp experiments in striated muscle fibres, The Journal of Physiology 208 (3) (1970) 607–644.
  • J. L. Hindmarsh, R. M. Rose, A. F. Huxley, A model of neuronal bursting using three coupled first order differential equations, Proceedings of the Royal Society of London. Series B. Biological Sciences 221 (1222) (1984) 87–102.
  • E. Izhikevich, Simple model of spiking neurons, IEEE Transactions on Neural Networks 14 (6) (2003) 1569–1572.
  • M. J. Chacron, A. Longtin, K. Pakdaman, Chaotic firing in the sinusoidally forced leaky integrate-and-fire model with threshold fatigue, Physica D: Nonlinear Phenomena 192 (1) (2004) 138–160.
  • H. Hayashi, S. Ishizuka, M. Ohta, K. Hirakawa, Chaotic behavior in the onchidium giant neuron under sinusoidal stimulation, Physics Letters A 88 (8) (1982) 435–438.
  • Y. Manor, J. Gonczarowski, I. Segev, Propagation of action potentials along complex axonal trees. model and implemen- tation, Biophysical journal 60 (6) (1991) 1411–1423.
  • L. Gammaitoni, P. Ha¨nggi, P. Jung, F. Marchesoni, Stochastic resonance, Reviews of modern physics 70 (1) (1998) 223.
  • D. F. Russell, L. A. Wilkens, F. Moss, Use of behavioural stochastic resonance by paddle fish for feeding, Nature 402 (6759) (1999) 291–294.
  • J. K. Douglass, L. Wilkens, E. Pantazelou, F. Moss, Noise enhancement of information transfer in crayfish mechanore- ceptors by stochastic resonance, Nature 365 (6444) (1993) 337–340.
  • S. Lu, Q. He, J. Wang, A review of stochastic resonance in rotating machine fault detection, Mechanical Systems and Signal Processing 116 (2019) 230–260.
  • B. McNamara, K. Wiesenfeld, Theory of stochastic resonance, Physical review A 39 (9) (1989) 4854.
  • A. Palonpon, J. Amistoso, J. Holdsworth, W. Garcia, C. Saloma, Measurement of weak transmittances by stochastic resonance, Optics letters 23 (18) (1998) 1480–1482.
  • E. Yilmaz, M. Uzuntarla, M. Ozer, M. Perc, Stochastic resonance in hybrid scale-free neuronal networks, Physica A: Statistical Mechanics and its Applications 392 (22) (2013) 5735–5741.
  • B. S. Gutkin, J. Jost, H. C. Tuckwell, Inhibition of rhythmic neural spiking by noise: the occurrence of a minimum in activity with increasing noise, Naturwissenschaften 96 (2009) 1091–1097.
  • D. Guo, Inhibition of rhythmic spiking by colored noise in neural systems, Cognitive neurodynamics 5 (2011) 293–300.
  • H. C. Tuckwell, J. Jost, The effects of various spatial distributions of weak noise on rhythmic spiking, Journal of Com- putational Neuroscience 30 (2011) 361–371.
  • D. Yu, Y. Wu, Z. Ye, F. Xiao, Y. Jia, Inverse chaotic resonance in hodgkin–huxley neuronal system, The European Physical Journal Special Topics 231 (22) (2022) 4097–4107.
  • H. Van Der Loos, E. M. Glaser, Autapses in neocortex cerebri: synapses between a pyramidal cell’s axon and its own dendrites, Brain research 48 (1972) 355–360.
  • M. R. Park, J. W. Lighthall, S. T. Kitai, Recurrent inhibition in the rat neostriatum, Brain research 194 (2) (1980) 359–369.
  • R. Preston, G. Bishop, S. Kitai, Medium spiny neuron projection from the rat striatum: an intracellular horseradish peroxidase study, Brain research 183 (2) (1980) 253–263.
  • A. B. Karabelas, D. P. Purrura, Evidence for autapses in the substantia nigra, Brain research 200 (2) (1980) 467–473.
  • R. Saada, N. Miller, I. Hurwitz, A. J. Susswein, Autaptic excitation elicits persistent activity and a plateau potential in a neuron of known behavioral function, Current Biology 19 (6) (2009) 479–484.
  • G. C. Sethia, J. Kurths, A. Sen, Coherence resonance in an excitable system with time delay, Physics Letters A 364 (3-4) (2007) 227–230. V. Baysal, E. Yılmaz, M. O¨ zer, Blocking of weak signal propagation via autaptic transmission in scale-free networks, IU-Journal of Electrical & Electronics Engineering 17 (1) (2017) 3091–3096.
  • Y. Li, G. Schmid, P. Ha¨nggi, L. Schimansky-Geier, Spontaneous spiking in an autaptic hodgkin-huxley setup, Physical Review E 82 (6) (2010) 061907.
  • H. Qin, J. Ma, C. Wang, R. Chu, Autapse-induced target wave, spiral wave in regular network of neurons, Science China Physics, Mechanics & Astronomy 57 (2014) 1918–1926.
  • H. Wang, J. Ma, Y. Chen, Y. Chen, Effect of an autapse on the firing pattern transition in a bursting neuron, Communi- cations in Nonlinear Science and Numerical Simulation 19 (9) (2014) 3242–3254.
  • E. Yilmaz, V. Baysal, M. Ozer, M. Perc, Autaptic pacemaker mediated propagation of weak rhythmic activity across small-world neuronal networks, Physica A: Statistical Mechanics and its Applications 444 (2016) 538–546.
  • C. Morris, H. Lecar, Voltage oscillations in the barnacle giant muscle fiber, Biophysical journal 35 (1) (1981) 193–213.
  • M. Uzuntarla, Inverse stochastic resonance induced by synaptic background activity with unreliable synapses, Physics Letters A 377 (38) (2013) 2585–2589.
  • E. Yilmaz, M. Ozer, Delayed feedback and detection of weak periodic signals in a stochastic hodgkin–huxley neuron, Physica A: Statistical Mechanics and its Applications 421 (2015) 455–462.
  • V. Baysal, Z. Sarac¸, E. Yilmaz, Chaotic resonance in hodgkin–huxley neuron, Nonlinear Dynamics 97 (2019) 1275– 1285.
  • W. Maass, Networks of spiking neurons: the third generation of neural network models, Neural networks 10 (9) (1997) 1659–1671.
  • D. Zhao, Y. Zeng, Y. Li, Backeisnn: A deep spiking neural network with adaptive self-feedback and balanced excitatory– inhibitory neurons, Neural Networks 154 (2022) 68–77.
There are 37 citations in total.

Details

Primary Language English
Subjects Theory of Computation (Other)
Journal Section Research Article
Authors

Ali Akçay This is me

Ergin Yılmaz

Publication Date August 2, 2024
Submission Date May 9, 2024
Acceptance Date June 5, 2024
Published in Issue Year 2024 Volume: 2 Issue: 1

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