Synchronization dynamics of two coupled neural oscillators receiving shared and unshared noisy stimuli
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
The response of neurons to external stimuli greatly depends on the intrinsic dynamics of the network. Here, the intrinsic dynamics are modeled as coupling and the external input is modeled as shared and unshared noise. We assume the neurons are repetitively firing action potentials (i.e., neural oscillators), are weakly and identically coupled, and the external noise is weak. Shared noise can induce bistability between the synchronous and anti-phase states even though the anti-phase state is the only stable state in the absence of noise. We study the Fokker-Planck equation of the system and perform an asymptotic reduction ρ 0. The ρ 0 solution is more computationally efficient than both the Monte Carlo simulations and the 2D Fokker-Planck solver, and agrees remarkably well with the full system with weak noise and weak coupling. With moderate noise and coupling, ρ 0 is still qualitatively correct despite the small noise and coupling assumption in the asymptotic reduction. Our phase model accurately predicts the behavior of a realistic synaptically coupled Morris-Lecar system.
- Apfaltrer, F., Ly, C., & Tranchina, D. (2006). Population density methods for stochastic neurons with a 2-D state space: Application to neural networks with realistic synaptic kinetics. Network: Computation in Neural Systems, 17, 373–418. CrossRef
- Arieli, A., Sterkin, A., Grinvald, A., & Aertsen, A. (1996). Dynamics of ongoing activity: Explanation of the large variability in evoked cortical responses. Science, 273, 1868. CrossRef
- Doiron, B., Chacron, M., Maler, L., Longtin, A., & Bastain, J. (2003). Inhibitory feedback required for network oscillatory responses to communication but not prey stimuli. Nature, 421, 539–543. CrossRef
- Doiron, B., Lindner, B., Longtin, A., Maler, L., & Bastian, J. (2004). Oscillatory activity in electrosensory neurons increases with spatial correlation of the stochastic input stimulus. Physical Review Letters, 93, 048101. CrossRef
- Ermentrout, G., & Kopell, N. (1991). Multiple pulse interactions and averaging in systems of coupled neural oscillators. Journal of Mathematical Biology, 29, 195–217. CrossRef
- Ermentrout, G. B. (1996). Type I membranes, phase-resetting curves, and synchrony. Neural Computation, 8, 979–1001. CrossRef
- Ermentrout, G. B. (2002). Simulating, analyzing, and animating dynamical systems: A guide to XPPAUT for researchers and students. Philadelphia: SIAM.
- Ferster, D., & Miller, K. (2000). Neural mechanisms of orientation selectivity in the visual cortex. Annual Review of Neuroscience, 23, 441–471. CrossRef
- Galán, R., Ermentrout, G. B., & Urban, N. N. (2007). Stochastic dynamics of uncoupled neural oscillators: Fokker-planck studies with the finite element method. Physical Review E, 76, 056110. CrossRef
- Galán, R., Fourcaud, N., Ermentrout, G. B., & Urban, N. N. (2006). Correlation-induced synchronization of oscillations in olfactory bulb neurons. Journal of Neuroscience, 26, 3646–3655. CrossRef
- Gardiner, C. W. (2004). Handbook of stochastic methods. New York: Springer Complexity.
- Gutkin, B., Laing, C., Colby, C., Chow, C., & Ermentrout, G. B. (2001). Turning on and off with excitation: The role of spike-timing asynchrony and synchrony in sustained neural activity. Journal of Computational Neuroscience, 11, 121–134. CrossRef
- Haider, B., Duque, A., Hasenstaub, A., Yu, Y., & McCormick, D. (2007). Enhancement of visual responsiveness by spontaneous local network activity in vivo. Journal of Neurophysiology, 97, 4186. CrossRef
- Hinrichsen, D., & Pritchard, A. (2005). Mathematical systems theory I, texts in applied mathematics (Vol. 48, pp. 340–372). New York: Springer.
- Hoppensteadt, F., & Izhekevich, I. (1997). Weakly connected neural networks. New York: Springer.
- Kanamaru, T. (2006). Analysis of Synchronization between two modules of pulse neural networks with excitatory and inhibitory connections. Neural Computation, 18, 1111–1131. CrossRef
- Kanamaru, T., & Sekine, M. (2005). Synchronized firings in the networks of class 1 excitable neurons with excitatory and inhibitory connections and their dependences on the forms of interactions. Neural Computation, 17, 1315–1338. CrossRef
- Kuramoto, Y. (1984). Chemical oscillations, waves and turbulence. New York: Springer.
- Ly, C., & Tranchina, D. (2007). Critical analysis of dimension reduction by a moment closure method in a population density approach to neural network modeling. Neural Computation, 19, 2032–2092. CrossRef
- MacLean, J., Watson, B., Aaron, G., & Yuste, R. (2005). Internal dynamics determine the cortical response to thalamic stimulation. Neuron, 48, 811–823. CrossRef
- Marella, S., & Ermentrout, G. B. (2008). Class-II neurons display a higher degree of stochastic synchronization than class-I neurons. Physical Review E, 77, 41918. CrossRef
- Morris, C., & Lecar, H. (1981). Voltage oscillations int he barnacle giant muscle fiber. Biophysical Journal, 193, 193–213. CrossRef
- Nakao, H., Arai, K., & Kawamura, Y. (2007). Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators. Physical Review Letters, 98, 184101. CrossRef
- Papanicolaou, G. (1977). Introduction to asymptotic analysis of stochastic equations. In R. C. DiPrima (Ed.), Modern modeling of continuum phenomena (Vol. 16, pp. 109–148). Providence: American Mathematical Society.
- Pfeuty, B., Mato, G., Golomb, D., & Hansel, D. (2005). The combined effects of inhibitory and electrical synapses in synchrony. Neural Computation, 17, 633–670. CrossRef
- Singer, W., & Strategies, T. (1999). Neuronal synchrony: A versatile code review for the definition of relations? Neuron, 24, 49–65. CrossRef
- Teramae, J., & Tanaka, D. (2004). Robustness of the noise-induced phase synchronization in a general class of limit cycle oscillators. Physical Review Letters, 93, 204103. CrossRef
- Tsodyks, M., Kenet, T., Grinvald, A., & Arieli, A. (1999). Linking spontaneous activity of single cortical neurons and the underlying functional architecture. Science, 286, 1943. CrossRef
- Winfree, A. (1974). Patteras of phase compromise in biological cycles. Journal of Mathematical Biology, 1, 73–93. CrossRef
- Synchronization dynamics of two coupled neural oscillators receiving shared and unshared noisy stimuli
Journal of Computational Neuroscience
Volume 26, Issue 3 , pp 425-443
- Cover Date
- Print ISSN
- Online ISSN
- Springer US
- Additional Links
- Neural oscillators
- Shared noise
- Weak coupling
- Weak noise
- Industry Sectors