Optimal inputs for phase models of spiking neurons

Journal of Computational and Nonlinear Dynamics

Volumn 1, Issue 4, 2006, Pages 358-367

  Moehlis, Jeff ^a   Shea Brown, Eric ^b   Rabitz, Herschel ^c  

^a University of California   (United States)

^b NEW YORK UNIVERSITY   (United States)

^c PRINCETON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COUPLINGS; NEUROLOGY; VARIATIONAL TECHNIQUES;

NEURAL OSCILLATOR MODELS; PHASE REDUCTIONS; SPIKING NEURONS;

OSCILLATORS (MECHANICAL);

EID: 33751086992     PISSN: 15551423     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2338654     Document Type: Article

References (24)

1. Ashwin, P., and Swift, J., 1992, "The Dynamics of N Weakly Coupled Identical Oscillators," J. Nonlinear Sci., 2, pp. 69-108.
2. Brown, E., Holmes, P., and Moehlis, J., 2003, "Globally Coupled Oscillator Networks," in Problems and Perspectives in Nonlinear Science: A Celebratory Volume in Honor of Lawrence Sirovich, E. Kaplan, J. E. Marsden, and K. R. Sreenivasan, eds., Springer, New York, pp. 183-215.
3. Cohen, A., Holmes, P., and Rand, R. H., 1982, "The Nature of Coupling Between Segmental Oscillators of the Lamprey Spinal Generator for Locomotion: A Model," J. Math. Biol., 13, pp. 345-369.
4. Gerstner, W., van Hemmen, L., and Cowan, J., 1996, "What Matters in Neuronal Locking?" Neural Comput., 8, pp. 1653-1676.
5. Ghigliazza, R. M., and Holmes, P., 2004, "A Minimal Model of a Central Pattern Generator and Motoneurons for Insect Loco-Motion," SIAM J. Appl. Dyn. Syst., 3(4), pp. 671-700.
6. Hansel, D., Mato, G., and Meunier, C., 1993, "Phase Dynamics for Weakly Coupled Hodgkin-Huxley Neurons," Europhys. Lett., 25(5), pp. 367-372.
7. Kopell, N., and Ermentrout, G. B., 1990, "Phase Transitions and Other Phenomena in Chains of Coupled Oscillators," SIAM J. Math. Anal., 50, pp. 1014-1052.
8. Taylor, D., and Holmes, P., 1998, "Simple Models for Excitable and Oscillatory Neural Networks," J. Math. Biol., 37, pp. 419-446.
9. Brown, E., Moehlis, J., and Holmes, P., 2004, "On the Phase Reduction and Response Dynamics of Neural Oscillator Populations," Neural Comput., 16, pp. 673-715.
10. Brown, E., Moehlis, J., Holmes, P., Clayton, E., Rajkowski, J., and Aston-Jones, G., 2004, "The Influence of Spike Rate and Stimulus Duration on Noradrenergic Neurons," J. Comput. Neurosci., 17, pp. 13-29.
11. Tass, P. A., 1999, Phase Resetting in Medicine and Biology, Springer, New York.
12. Rieke, F., Warland, D., de Ruyter van Steveninck, R., and Bialek, W., 1996, Spikes: Exploring the Neural Code, MIT Press, Cambridge, MA.
13. Forger, D. B., and Paydarfar, D., 2004, "Starting, Stopping, and Resetting Biological Oscillators: In Search of Optimal Perturbations," J. Theor. Biol., 230, pp. 521-532.
14. Tuckwell, H., and Feng, J., 2005, "Optimal Control of Neuronal Activity," Phys. Rev. Lett., 91, p. 018101.
15. Winfree, A., 2001, The Geometry of Biological Time, 2nd ed., Springer, New York.
16. Bryson, A., and Ho, Y., 1975, Applied Optimal Control, Halsted Press, Washington, DC.
17. Goldstein, H., 1980, Classical Mechanics, 2nd ed., Addison-Wesley, Reading, MA.
18. Ermentrout, G. B., 1996, "Type I Membranes Phase Resetting Curves, and Synchrony," Neural Comput., 8, pp. 979-1001.
19. Ermentrout, G. B., and Kopell, N., 1984, "Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I," SIAM J. Math. Anal., 15, pp. 215-237.
20. Hodgkin, A. L., and Huxley, A. F., 1952, "A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve," J. Physiol. (London), 117, pp. 500-544.
21. Ermentrout, G. B., 2002, Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, SIAM, Philadelphia.
22. Herrmann, A., and Gerstner, W., 2001, "Noise and the PSTH Response to Current Transients: I. General Theory and Application to the Integrate-and-Fire Neuron," J. Comput. Neurosci., 11, pp. 135-151.
23. Aguera y Areas, B., Fairhall, A., and Bialek, W., 2003, "Computation in a Single Neuron: Hodgkin and Huxley Revisited," Neural Comput., 15, pp. 1715-1749.
24. Rothman, A., Ho, T.-S., and Rabitz, H., 2006, "Exploring Level Sets of Quantum Control Landscapes," Phys. Rev. A 73, p. 053401.