Dynamics of electric activities in neuron and neurons of network induced by autapses

Science China Technological Sciences

Volumn 57, Issue 5, 2014, Pages 936-946

  Qin, Huixin ^a   Ma, Jun ^a   Jin, Wuyin ^a   Wang, Chunni ^a  

^a LANZHOU UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

bifurcation; Lyapunov exponent; network; neuron; time delay

Indexed keywords

BIFURCATION (MATHEMATICS); FEEDBACK; LYAPUNOV METHODS; NETWORKS (CIRCUITS); TIME DELAY;

ELECTRIC ACTIVITY; FEEDBACK GAIN; H-R NEURONS; HINDMARSH-ROSE NEURONS; LYAPUNOV EXPONENT; PARAMETER REGIONS; TIME DELAYED COUPLING; TIME-DELAYED FEEDBACK;

NEURONS;

EID: 84901022655     PISSN: 16747321     EISSN: 18691900     Source Type: Journal    
DOI: 10.1007/s11431-014-5534-0     Document Type: Article

References (62)

1. Morris C, Lecar H. Voltage oscillations in the brain giant muscle fiber. Biophys J, 1981, 35: 193-213
2. Jaeger J, Czobor P, Berns S M. Basic neuropsychological dimensions in schizophrenia. Schizophrenia Res, 2011, 130: 86-93
3. Hermann B P. Imaging Epilepsy. J Int Neuropsychol Soc, 2006, 12: 154-156
4. Baxter P. Epilpsy and sleep. Develop Med Child Neurol, 2005, 47: 723
5. Seidman L J, Sone W S, Jones R, et al. Comparative effects of schizophrenia and temporal lobe epilepsy on memory. J Int Neuropsychol Soc, 2000, 4: 342-352
6. Labar D. Developmental medicine & child neurology. Develop Med Child Neurol, 2000, 42: 496-499
7. Johnston A, Smith A. Epilepsy in the older patient. Rev Clinical Gerontol 2007, 17: 109-118
8. Jia B, Gu H G, Song S L. Experimental researches on different complex bifurcation procedures of neural firing patterns. Sci China Phys Mech, 2013, 43: 518-523
9. Allen N J, Barres B A. Glia-more than just brain glue. Neurosci 2009, 475: 675-677
10. Barres B A. The mystery and magic of glia: a perspective on their roles in health and disease. Neuron, 2008, 60: 430-440
11. Postnov D E, Ryazanova L S, Brazhe N A, et al. Giant Glial Cell: New Insight Through Mechanism-Based Modeling. J Biol Phys, 2008, 34: 441-457
12. Postnov D E, Ryazanova L S, Sosnovtseva O S. Functional modeling of neuralglial interaction. BioSystems, 2007, 89: 84-91
13. Wang R B, Zhang Z K. Energy coding and energy functions for local activities of the brain. Neucomput, 2009, 73: 139-150
14. Wang R B, Zhang Z K, Chen G R. Energy function and energy evolution on neuronal populations. IEEE Tra Neu Network, 2008, 19: 535-538
15. Wang R B, Zhang Z K. Energy coding in biological neural networks. Cogn Neurodyn, 2007, 1: 203-212
16. Fromherz P, Müller C O. Cable properties of a straight neurite of a leech neuron probed by a voltage-sensitive dye. PNAS, 1994, 91: 4604-4608
17. Tsumoto K, kitajima H, Yoshinaga T, et al. Bifurcations in Morris-Lecar neuron model. Neucomput, 2006, 69: 293-316
18. Barland S, Piro O, Giudici M, et al. Experimental evidence of van der Pol-Fitzhugh-Nagumo dynamics in semiconductor optical amplifiers. Phys Rev E, 2003, 68: 036209
19. Nakayama T. Thermosensitive Neurons in the Brain. Jap J Physiol, 1985, 35: 375-389
20. Hindmarsh J L, Rose R M. A model of the nerve impulse using two first-order differential equations. Nature (London), 1982, 276: 162-164
21. Wang C N, Ma J, Jin W Y. Identification of parameters with different orders of magnitude in chaotic systems. Dynam Syst, 2012, 27: 253-270
22. Yu H J, Tong W J. Chaotic control of hindmarsh-rose neuron by delayed self-feedback. Acta Phys Sin, 2009, 58: 2977-2982
23. Shi X. Burst Synchronization of Coupled Neurons by Chemical Synapses. Chin Quarterly Mech, 2010, 31: 52-57
24. Lacasta A M, Sagués, Sancho J M. Coherence and anticoherence resonance tuned by noise. Phy Rev E, 2002, 66: 045105
25. Baltana's J P, Caado J M. Noise-induced resonances in the Hindmarsh-Rose neuronal model. Phys Rev E, 2002, 65: 041915
26. Chik D T W, Wang Y Q, Wang Z D. Stochastic resonance in a Hodgkin-Huxley neuron in the absence of external noise. Phys Rev E, 2001, 64: 021913
27. Yu Y G, Wang W, Wang J F, et al. Resonance-enhanced signal detection and transduction in the Hodgkin-Huxley neuronal systems. Phys Rev E, 2001, 63: 021907
28. Liu F, Wang J F, Wang W. Frequency sensitivity in weak signal detection. Phys Rev E 1999, 59: 3453-3460
29. Perc M. Spatial coherence resonance in excitable media. Phys Rev E, 2005, 72: 016207
30. Perc M. Spatial coherence resonance in neuronal media with discrete local dynamics. Chaos, Solitons & Fractals, 2007, 31: 64-69
31. Gosak M, Marhl M, Perc M. Spatial coherence resonance in excitable biochemical media induced by internal noise. Biophys Chem, 2007, 128: 210-214
32. Zhang J Q, Shen C S, Cui Z F. Modulation on the collective response behavior by the system size in two-dimensional coupled cell systems. Sci China Ser G-Phys Mech Astron, 2006, 49: 304-312
33. Zhou C S, Kurth J. Noise-induced synchronization and coherence resonance of a Hodgkin-Huxley model of thermally sensitive neurons. Chaos, 2003, 13: 401-409
34. Zhang J Q, Wang C D, Wang M S, et al. Firing patterns transition induced by system size in coupled Hindmarsh-Rose neural system. Neurocomput, 2011, 74: 2961-2966
35. Perc M. Stochastic resonance on excitable small-world networks via a pacemaker. Phys Rev E, 2007, 76: 066203
36. Wang Q Y, Perc M, Duan Z S, et al. Delay-enhanced coherence of spiral waves in noisy Hodgkin-Huxley neuronal networks. Phys Lett A, 2008, 372: 5681-5687
37. Wang Q Y, Perc M, Duan Z S, et al. Delay-induced multiple stochastic resonances on scale-free neuronal networks. Chaos, 2009, 19: 023112
38. Liu Z Q, Zhang H M, Li Y L, et al. Multiple spatial coherence resonance induced by stochastic signal in neuronal networks near a saddle-node bifurcation. Physica A, 2010, 389: 2642-2653
39. Wu X Y, Ma J. The Formation Mechanism of Defects, Spiral Wave in the Network of Neurons. Plos One, 2013, 8:55403
40. Hu B L, Ma J, Tang J. Selection of Multiarmed spiral waves in a regular network of neurons. PLOS ONE, 2013, 8: 69251
41. Ma J, Huang L, Wang C N, et al. Robustness, Death of Spiral Wave in the Network of Neurons under Partial Ion Channel Block. Commun Theor Phys, 2013, 59: 233-242
42. Wu X Y, Ma J. Development of spiral wave in a regular network of excitatory neurons due to stochastic poisoning of ion channels. Commun Nonlinear Sci Numer Simulat, 2013, 18: 3350-3364
43. Ma J, Wu Y, Wu N J, et al. Detection of ordered wave in the networks of neurons with changeable connection. Sci China Phys Mech Astro, 2013, 56: 952-959
44. Ma J, Wu Y, Ying H P, et al. Channel noise-induced phase transition of spiral wave in networks of Hodgkin-Huxley neurons. Chin Sci Bull, 2011, 56: 151-157
45. Ma J, Zhang A H, Tang J, et al. Robustness and breakup of the spiral wave in a two-dimensional lattice network of neurons. Sci China Phys Mech Astro, 2010, 53: 672-679
46. Joachim L, Henry M, Michael F, et al. 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. J Neurosci, 1996, 16: 3209-3218
47. Nägler K, Mauch D H, Pfrieger F W. Glia-derived signals induce synapse formation in neurons of the rat central nervous system. J Physiol, 2001, 533: 665-679
48. Herrmann C S, Klaus A. Autapse Turns Neuron into Oscillator. Int J Bifurcat Chaos, 2004, 14: 623-633
49. Ullian E M, Harris B T, Wu A, et al. Schwann cells and astrocytes induce synapse formation by spinal motor neurons in culture. Mol Cell Neurosci, 2004, 25: 241-251
50. Fan Y T, Xu F, Huang G Y, et al. Single neuron capture and axonal development in three-dimensional microscale hydrogels. Lab Chip, 2012, 12: 4724-4731
51. Bekkers J M. Synaptic Transmission: Functional Autapses in theCortex. Current Biology, 2003, 13: 433-435
52. Seung H S. The Autapse: A Simple Illustration of Short-Term Analog Memory Storage by Tuned Synaptic Feedback. J Comput Neurosci, 2000, 9: 171-185
53. Sgro A E, Nowak A L, Austin N S, et al. A high-throughput method for generating uniform microislands for autaptic neuronal cultures. J Neurosc Methods, 2011, 198: 230-235
54. Yun Y L, Schmid G, Hänggi P, et al. Spontaneous spiking in an autaptic Hodgkin-Huxley setup. Phys Rev E, 2010, 82: 061907
55. Wang H T, Chen Y L, Chen Y, et al. Autapse affect Firing Patterns Transition in Bursting Neuron. Commun Nonlinear Sci Numer Simulat, 2013
56. Belykh I, de Lange E, Hasler M. Synchronization of Bursting Neurons: What Matters in the Network Topology. Phys Rev Lett, 2005, 94: 118101
57. Gu HG, Yang M H, Li L, et al. Dynamics of autonomous stochastic resonance in neural period-adding bifurcation scenarios. Phys Lett A, 2003, 319: 89-96;.
58. Channell P, Cymbalyuk G, Shilnikov A. Origin of bursting through homoclinic spike adding in a neuron model. Phys Rev Lett, 2007, 98: 134101
59. González-Miranda J. Complex bifurcation structures in the Hindmarsh-Rose neuron model. Int J Bifurcat Chaos, 2007, 17: 3071-3083
60. Mo J, Li Y Y, Wei C L, et al. Interpreting a period-adding bifurcation scenario in neural bursting patterns using border-collision bifurcation in a discontinuous map of a slow control variable. Chin Phys B, 2010, 19: 080513
61. Linaro D, Champneys A, Desroches M, et al. Codimension-two homoclinic bifurcations underlying spike adding in the Hindmarsh-Rose burster. SIAM J Appl Dyn Syst, 2012, 11: 939-962
62. Gu H G, Jia B, Chen G R. Experimental evidence of a chaotic region in a neural pacemaker. Phys Lett A, 2013, 377: 718-720