Control of multistability in ring circuits of oscillators

Biological Cybernetics

Volumn 80, Issue 2, 1999, Pages 87-102

  Canavier, C C ^a   Baxter, D A ^b   Clark, J W ^c   Byrne, J H ^b  

^a UNIVERSITY OF NEW ORLEANS   (United States)

^b UNIVERSITY OF TEXAS MEDICAL SCHOOL   (United States)

^c Rice University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0002912059     PISSN: 03401200     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004220050507     Document Type: Article

References (23)

1. Baxter DA, Canavier CC, Lechner HA, Butera RJ, DeFranceschi AA, Clark JW, Byrne JH (in press) Coexisting stable oscillatory states in single cell and multicellular neuronal oscillators. In: Levine D, Brown V, Shirey T (eds) Oscillations in neural systems. Lawrence Erlbaum, Englewood Cliffs (in press)
2. Butera RJ Jr, Canavier CC, Baxter DA, Clark JW, Byrne JH (1995) Analysis of the effects of modulatory agents on a model bursting neuron: dynamic interactions between voltage and calcium-dependent systems. J Comp Neurosci 2:19-44
3. Canavier CC, Butera RJ, Dror RO, Baxter DA, Clark JW, Byrne JH (1997) Phase response characteristics of model neurons determine which patterns are expressed in a ring circuit model of gait generation. Biol Cybern 77:367-380
4. Collins JJ, Richmond SA (1994) Hard-wired central pattern generators for quadrupedal locomotion. Biol Cybern 71:371-385
5. Collins JJ, Stewart IN (1993) Coupled nonlinear oscillators and the symmetries of animal gaits. J Nonlinear Sci 3:349-392
6. Collins JJ, Stewart IN (1994) A group-theoretic approach to rings of coupled biological oscillators. Biol Cybern 71:95-103
7. DeFranceschi AA (1995) A phase sensitivity based method for prediction of modes of behavior in quadrupedal locomotion. Master's thesis, Rice University
8. Dror RO, Canavier CC, Butera RJ, Clark JW, Byrne JH (1999) A mathematical criterion based on phase-response curves for the stability of a ring network of oscillators. Biol Cybern 80:11-23
9. Ermentrout GB (1985) The behavior of rings of coupled oscillators. J Math Biol 23:55-74
10. Ermentrout GB, Kopell N (1991) Multiple pulse interactions and averaging in systems of coupled neural oscillators. J Math Biol 29:195-217
11. Grillner S. (1975) Locomotion in vertebrates: central mechanisms and reflex interaction. Physiol Rev 55:247-306
12. Hairer E, Wanner G (1991) Solving ordinary differential equations II. Stiff and differential-algebraic problems. (Springer Series in Computational Mathematics) Springer, Berlin Heidenberg New York
13. Harris-Warrick RM, Marder E (1991) Modulation of neural networks for behavior. Annu Rev Neurosci 14:39-58
14. Harris-Warrick RM, Baro DJ, Coniglio LM, Johnson BR, Levini RM, Peck JH, Zhang B (1997) Chemical modulation of crustacean stomatogastric pattern generator networks. In: Stein PSG, Grillner S, Selverston AI, Stuart DG (eds) Oscillations in neural systems MIT Press, Cambridge, Mass
15. Holst Ev (1973) The behavioral physiology of animals and man: the collected papers of Erich von Holst. University of Miami Press, Coral Gables
16. Kopell N (1988) Towards a theory of modelling generators. In: Cohen AH, Rossignol S, Grillner S (eds) Neural control of rhythmic movements in vertebrates. Wiley, New York, pp 369-413
17. Kopell N, Ermentrout GB (1988a) Coupled oscillators and the design of central pattern generators. Math Biosci 90:87-109
18. Kopell N, Ermentrout GB (1988b) Symmetry and phaselocking in chains of weakly coupled oscillators. Commun Pure App Math 90:87-109
19. Murray JD (1989) Mathematical biology. Springer, Berlin Heidelberg Newyork
20. Pasemann F (1995) Characterization of periodic attractors in neural ring networks. Neural Networks 8:421-429
21. Pavlides T (1973) Biological oscillators: their mathematical analysis. Academic Press, New York
22. Pearson K (1993) Common principles of motor control in vertebrates and invertebrates. Annu Rev Neurosci 16:265-297
23. Selverston AI (1980) Are central pattern generators understandable? Behav Brain Sci 3:535-571