Synchronization study in ring-like and grid-like neuronal networks

Cognitive Neurodynamics

Volumn 6, Issue 1, 2012, Pages 21-31

  Qu, Jingyi ^a   Wang, Rubin ^a   Du, Ying ^a   Cao, Jianting ^a  

^a EAST CHINA UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

Author keywords

Bifuration diagram; Correlation coefficient; ISI distance; Mean field potential; Ring like and grid like neuronal network

Indexed keywords

ARTICLE; CELL SYNCHRONIZATION; GAP JUNCTION; MATHEMATICAL ANALYSIS; NERVE CELL; NERVE CELL NETWORK;

EID: 84860837149     PISSN: 18714080     EISSN: 18714099     Source Type: Journal    
DOI: 10.1007/s11571-011-9174-9     Document Type: Article

References (38)

1. Braun HA, Huber MT, Anthes N, Voigt K, Neiman A, Moss F (2001) Noise induced impulse pattern modifications at different dynamical period-one situations in a computer-model of temperature encoding. Biosystems 62:99-112 (Pubitemid 32930043)
2. Braun HA, Huber MT, Anthes N, Voigt K, Neiman A, Pei X, Moss F (2000) Interactions between slow and fast conductances in the Huber/Braun model of cold receptor discharges. Neurocomputing 32 (33):61-66
3. Braun HA, Schäfer K, Voigt K, Huber MT (2003) Temperature encoding in peripheral cold receptors: oscillations, resonances,chaos and noise. Nonlinear Dyn Spatiotemp Princ Biol 88 (332):293-18
4. Che YQ, Wang J, Tsang KM, Chan WL (2010) Unidirectional synchronization for Hindmarsh-Rose neurons via robust adaptive sliding mode control. Nonlinear Anal Real World Appl11:1096-1104
5. De Vries G, Sherman A (2001) From spikes to bursters via coupling: help from heterogeneity. Bull Math Boil 63:371-391 (Pubitemid 32577713)
6. Du Y, Lu QS, Wang RB (2010) Using interspike intervals to quantify noise effects on spike trains in temperature encoding neurons. Cogn Neurodyn 4:199-206
7. Finke C, Vollmer J, Postnova S, Braun HA (2008) Propagation effects of current and conductance noise in a model neuron withsubthreshold oscillations. Math Boisci 214:109-121
8. Freeman WJ (2000) Neurodynamics-an exploration in mesoscopic brain dynamics. Springer, London Gan QT, Xu R, Kang XB (2011) Synchronization of chaotic neural networks with mixed time delays. Commun Nonlinear SciNumer Simulat 16:966-974
9. Haas JS, Write JA (2002) Frequency selectivity of layer II stellate cells in the medial entorhinal cortex. J Neurophysiol88:2422-2429 (Pubitemid 35346047)
10. Haeri M, Dehghani M (2010) Modified impulsive synchronization of hyperchaotic systems. Commun Nonlinear Sci Numer Simulat 15:728-740
11. Haken H (2002) Brain dynamics-synchronization and activity patternsin pulse-coupled neural nets with delays and noise. Springer,Berlin
12. Hao YB, Gong YB, Lin X, Xie YH, Ma XG (2010) Transition and enhancement of synchronization by time delays in stochastic Hodgkin-Huxley neuron networks. Neurocomputing 73: 2998-3004
13. Hodgkin AL, Huxley AF (1952) A qualitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500-544
14. Huber MT, Braun HA (2006) Stimulus response curves of a neuronal model for noisy subthreshold oscillations and related spike generation. Phys Rev E 73 (41929):1-10
15. Huber MT, Braun HA (2007) Conductance versus current noise in a neuronal model for noisy subthreshold oscillations and spike generation. Biosystems 89 (1-3):38-43 (Pubitemid 46679101)
16. Kreuz T, Chicharro D, Andrzejak RG, Haas JS, Abarbanel HDI (2009) Multiple spike train synchrony. J Neurosci Meth 183:287-299
17. Kreuz T, Haas JS, Morelli A, Abarbanel HDI, Politi A (2007) Measuring spike train synchrony. J Neurosci Meth 165:151-161 (Pubitemid 47077507)
18. Liu XY, Cao JD (2011) Local synchronization of one-to-one coupled neural networks with discontinuous activations. Cogn Neurodyn 5 (1):13-20
19. Ma J, Li F, Huang L, Jin WY (2011) Complete synchronization, phase synchronization and parameters estimation in a realistic chaotic system. Commun Nonlinear Sci Numer Simulat 16:3770-3785
20. Nomura M, Fukai T, Aoyagi T (2003) Synchrony of fast-spiking interneurons interconnected by GABAergic and electrical synapses. Neural Comput 15:2179-2198 (Pubitemid 37035542)
21. Pikovsky A, Rosenblum M, Kurths J (2001) Synchronization, a universal concept in nonlinear sciences. Cambridge University Press, New York
22. Postnova S, Christian F, Jin W, Schneider H, Braun HA (2010) A computational study of the interdependencies between neuronal impulse pattern, noise effects and synchronization. J Physiol Paris 104:176-189
23. Postnova S, Voigt K, Braun HA (2007) Neural synchronization at tonic-to-bursting transitions. J Boil Phys 33:129-143 (Pubitemid 351326294)
24. Postnova S, Wollweber B, Voigt K, Braun HA (2007) Impulse-pattern in bidirectionally coupled model neurons of different dynamics. Biosystems 89 (1-3):135-142 (Pubitemid 46679114)
25. Sato YD, Shiino M (2007) Generalization of coupled spiking models and effects of the width of an action potential on synchronizationphenomena. Phys Rev E 75:011909-011915
26. Schreiber S, Fellous JM, Whitmer JH, Tiesinga PHE, Sejnowski TJ (2003) A new correlation-based measure of spike timingreliability. Neurocomputing 52:925-931 (Pubitemid 36700596)
27. Shi X, Wang QY, Lu QS (2008) Firing synchronization and temporal order in noisy neuronal networks. Cogn Neurodyn 2 (3):195-206
28. Shilnikov A, Cymbalyuk G (2005) Transition between tonic spiking and bursting in a neuron model via the blue-sky catastrophe. Phys Rev Lett 94:048101-041930
29. Shilnikov A, CalabreseG (2005)Mechanism of bistability: tonic spiking and bursting in a neuron model. Phys Rev E 71:056214-056219
30. Singer W (1994) Time as coding space in neocortical processing. Springer, Berlin
31. Sun WG, Wang RB, Wang WX, Cao JT (2010) Analyzing inner and outer synchronization between two coupled discrete-time networkswith time delays. Cogn Neurodyn 4 (3):225-231
32. Van Rossum MCW (2001) A novel spike distance. Neural Comput 13:751-763
33. Victor J, Purpura K (1996) Nature and precision of temporal coding in visual cortex: a metric-space analysis. J Neurophysiol 76:1310-1326 (Pubitemid 26284607)
34. Wang QY, Duan ZS, Feng ZS, Chen GR, Lu QS (2008) Synchronization transition in gap-junction-coupled leech neurons. Physica A 387:4404-4410
35. Wang QY, Lu QS, Duan ZS (2010) Adaptive lag synchronization in coupled chaotic systems with unidirectional delay feedback. Int J Non-Linear Mech 45:640-646
36. Wang XJ (1993) of bursting oscillations in the Hindmarsh-Rose model and homoclinicity to a chaotic saddle. Physica D 62:263-274
37. Yu WW, Cao JD, Lu WL (2010) Synchronization control of switched linearly coupled neural networks with delay. Neurocomputing 73:858-866
38. Zheng YH, Lu QS (2008) Spatiotemporal patterns and chaotic burst synchronization in a small-world neuronal network. Physica A 387:3719-3728