The calculation of frequency-shift functions for chains of coupled oscillators, with application to a network model of the Iamprey locomotor pattern generator

Journal of Computational Neuroscience

Volumn 4, Issue 1, 1997, Pages 47-55

  Williams, Thelma L ^a   Bowtell, Graham ^b  

^a ST GEORGE S HOSPITAL   (United Kingdom)

^b CITY UNIVERSITY   (United Kingdom)

Author keywords

Central pattern generator; Coupled oscillators; Iamprey spinal cord; Intersegmental coordination; Locomotion

Indexed keywords

OSCILLATORS (ELECTRONIC); OSCILLATORS (MECHANICAL);

CENTRAL PATTERN GENERATOR; COUPLED OSCILLATORS; COUPLED OSCILLATORS WITH; FREQUENCY SHIFT; IAMPREY SPINAL CORD; INTER-SEGMENTAL COORDINATION; LOCOMOTION; PATTERN GENERATOR; SHIFT FUNCTIONS; SPINAL-CORD;

CHAINS;

ALGORITHM; ARTICLE; CALCULATION; CYCLOSTOME; LOCOMOTION; NERVE CELL NETWORK; OSCILLATOR; PATTERN GENERATOR; PRIORITY JOURNAL; SIMULATION; SPINAL CORD;

EID: 0031040137     PISSN: 09295313     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008864410375     Document Type: Article

References (20)

1. Buchanan JT (1986) Premotor interneurons in the lamprey spinal cord: Morphology, synaptic interactions and activities during fictive swimming. In: S Grillner, PSG Stein, DG Stuart, H Forssberg, RM Herman, eds. Neurobiology of Vertebrate Locomotion. Macmillan, London, pp. 321-333.
2. Buchanan JT (1992) Neural network simulations of coupled locomotor oscillators in the lamprey spinal cord. Biol. Cybern. 66: 367-374.
3. Buchanan JT, Grillner S (1987) Newly identified "glutamate interneurons" and their role in locomotion in the lamprey spinal cord. Science 236: 312-314.
4. Cohen AH, Ermentrout GB, Kiemel T, Kopell N, Sigvardt KA, Williams TL (1993) Modelling of intersegmental coordination in the lamprey central pattern generator for locomotion. Trends Neurosci. 15: 434-438.
5. Cohen AH, Kiemel T (1993) Intersegmental coordination: Lessons from modeling systems of coupled non-linear oscillators. Amer. Zool. 35: 54-65.
6. Ermentrout GB, Kopell N (1984) Frequency plateaus in a chain of weakly coupled oscillators. SIAM J. Math, Anal. 15: 215-237.
7. Ermentrout GB, Kopell N (1991) Multiple pulse interactions and averaging in systems of coupled neural oscillators. J. Math. Biol. 29: 195-217.
8. Ferrar CH, Williams TL, Bowtell G (1993) The effects of cell duplication and noise in a pattern generating network. Neural Computation 5: 587-596.
9. Kopell N, Ermentrout GB (1986) Symmetry and phaselocking in chains of weakly coupled oscillators. Comm. Pure Appl. Math. 39: 623-660.
10. Kopell N, Ermentrout GB, Williams TL (1991) On chains of oscillators forced at one end. SIAM J. Appl. Math. 51: 1397-1417.
11. Kopell N, Zhang W, Ermentrout GB (1990) Multiple coupling in chains of oscillators. SIAM J. Math. Anal. 21: 935-953.
12. Mellen N, Kiemel T, Cohen AH (1995) Correlational analysis of fictive swimming in the lamprey reveals strong functional intersegmental coupling. J Neurophysiol. 73: 1020-1030.
13. Murray, JD (1989) Mathematical Biology. Berlin, Springer-Verlag.
14. Sigvardt KA (1993) Intersegmental coordination in the lamprey central pattern generator for locomotion. Seminars Neurosci. 5: 3-15.
15. Sigvardt KA, Williams TL (1996) Effects of local oscillator frequency on intersegmental coordination in the lamprey locomotor CPG: Theory and experiment. J. Neurophysiol. (in press).
16. Williams TL (1992a) Phase coupling in simulated chains of coupled oscillators representing the lamprey spinal cord. Neural Computation 4: 546-558.
17. Williams TL (1992b) Phase coupling by synaptic spread in chains of coupled neuronal oscillators. Science 258: 662-665.
18. Williams TL, Sigvardt KA (1994) Intersegmental phase lags in the lamprey spinal cord: Experimental confirmation of the existence of a boundary region. J. Computational Neurosci. 1: 61-67.
19. Williams TL, Sigvardt KA, Kopell N, Ermentrout GB, Remler MP (1990) Forcing of coupled nonlinear oscillators: Studies of intersegmental coordination in the lamprey locomotor central pattern generator. J. Neurophysiol. 64: 862-871.
20. Winfree AT (1980) The Geometry of Biological Time. Berlin, Springer-Verlag.