Effective desynchronization by means of double-pulse phase resetting

Europhysics Letters

Volumn 53, Issue 1, 2001, Pages 15-21

  Tass, P A ^a  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034747444     PISSN: 02955075     EISSN: None     Source Type: Journal    
DOI: 10.1209/epl/i2001-00117-6     Document Type: Article

References (40)

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19. Both a periodically firing or bursting neuron displays the dynamics of a limit cycle oscillator (for a review, see [3]) which is approximated by means of a phase oscillator [6]. Accordingly, neuronal populations are modeled as networks of oscillators; SCHUSTER H. G. and WAGNER P., Biol. Cybern., 64 (1990) 77; SCHUSTER H. G. and WAGNER P., Biol Cybern., 64 (1990) 83; SOMPOLINSKY H., GOLOMB D. and KLEINFELD D., Phys. Rev. A, 43 (1991) 6990; HANSEL D., MATO G. and MEUNIER C., Europhys. Lett., 23 (1993) 367; SCHILLEN T. B. and KÖNIG P., Biol. Cybern., 70 (1994) 397; TASS P. A. and HAKEN H., Biol. Cybern., 74 (1996) 31.
20. Both a periodically firing or bursting neuron displays the dynamics of a limit cycle oscillator (for a review, see [3]) which is approximated by means of a phase oscillator [6]. Accordingly, neuronal populations are modeled as networks of oscillators; SCHUSTER H. G. and WAGNER P., Biol. Cybern., 64 (1990) 77; SCHUSTER H. G. and WAGNER P., Biol Cybern., 64 (1990) 83; SOMPOLINSKY H., GOLOMB D. and KLEINFELD D., Phys. Rev. A, 43 (1991) 6990; HANSEL D., MATO G. and MEUNIER C., Europhys. Lett., 23 (1993) 367; SCHILLEN T. B. and KÖNIG P., Biol. Cybern., 70 (1994) 397; TASS P. A. and HAKEN H., Biol. Cybern., 74 (1996) 31.
21. Both a periodically firing or bursting neuron displays the dynamics of a limit cycle oscillator (for a review, see [3]) which is approximated by means of a phase oscillator [6]. Accordingly, neuronal populations are modeled as networks of oscillators; SCHUSTER H. G. and WAGNER P., Biol. Cybern., 64 (1990) 77; SCHUSTER H. G. and WAGNER P., Biol Cybern., 64 (1990) 83; SOMPOLINSKY H., GOLOMB D. and KLEINFELD D., Phys. Rev. A, 43 (1991) 6990; HANSEL D., MATO G. and MEUNIER C., Europhys. Lett., 23 (1993) 367; SCHILLEN T. B. and KÖNIG P., Biol. Cybern., 70 (1994) 397; TASS P. A. and HAKEN H., Biol. Cybern., 74 (1996) 31.
22. Both a periodically firing or bursting neuron displays the dynamics of a limit cycle oscillator (for a review, see [3]) which is approximated by means of a phase oscillator [6]. Accordingly, neuronal populations are modeled as networks of oscillators; SCHUSTER H. G. and WAGNER P., Biol. Cybern., 64 (1990) 77; SCHUSTER H. G. and WAGNER P., Biol Cybern., 64 (1990) 83; SOMPOLINSKY H., GOLOMB D. and KLEINFELD D., Phys. Rev. A, 43 (1991) 6990; HANSEL D., MATO G. and MEUNIER C., Europhys. Lett., 23 (1993) 367; SCHILLEN T. B. and KÖNIG P., Biol. Cybern., 70 (1994) 397; TASS P. A. and HAKEN H., Biol. Cybern., 74 (1996) 31.
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33. In the case of weaker (subcritical) stimulation other attractors occur which are, e.g., periodic in time [10]. For the numerical investigation a Fourier transformation of eq. (2) is performed, Fourier modes with wave numbers \k\ ≤ 200 are taken into account, and a 4th order Runge-Kutta algorithm with a time step of 0.0001 is used [10].
34. 1. Only one of these phase values is appropriate for a desynchronization. Generically, however, the single pulse hits the cluster at, a wrong initial phase, in this way synchronizing the cluster as in fig. 3a, b.
35. n from eq. (3) is the relevant variable that has to be desynchronized as in fig. 1e, f. This is most effectively achieved with a stimulus S containing terms of n-th order, e.g., S(ψ) = I cos(nψ).
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40. The right stimulation parameters are experimentally determined in a reliable way with a procedure which was developed for the single-pulse stimulation [10] and holds in the case of the double pulse, too. To this end, a series of test stimulations is performed, the phase of the dominant mode is extracted out of the experimetal data (with bandpass filtering and Hilbert transform), and, finally, phase resetting curves yield the right parameters.