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Spiking dynamics of interacting oscillatory neurons
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View: Figures


Image of FIG. 1.
FIG. 1.

(a) Phase portrait of the master unit dynamics. The unit has three fixed points and stable limit cycle corresponding to periodic spike train. (b) Excitable dynamics of the slave unit. The saddle separatrix defines the excitation threshold of the stable rest state .

Image of FIG. 2.
FIG. 2.

MFHN electronic circuits. Electrical parameters: , , , , , leading to and . , , , , and , leading to , . For the oscillating (master) unit we set: , . Parameters, for the excitable (slave) unit: , .

Image of FIG. 3.
FIG. 3.

Experimental phase portraits showing the dynamics of the master and slave units. (a) Stable limit cycle coexisted with stable fixed point in the master unit. Parameters: and ( and ). Inset: Spiking train of pulses (upper inset) corresponding to the limit cycle; perturbation reaching the stable fixed point (lower inset). Parameters of inset: abscissa ; ordinate . (b) Excitable behavior of the slave unit. Parameters: and ( and ). Insets: Excitation pulse (upper inset); perturbation reaching the stable fixed point without excitation (lower inset). Parameters of insets: abscissa ; ordinate .

Image of FIG. 4.
FIG. 4.

(a) Fragment of superimposed master and slave time series shown by dashed and solid curves, respectively. The spiking phase, , is defined as a time shift between master and slave oscillations peaks. Parameter values: , , . (b) Spiking phase diagram showing the phases located in the neighborhood of some piecewise continuous curve.

Image of FIG. 5.
FIG. 5.

Phase definition in the -plane. The master limit cycle is shown by dashed curve. The dots show the -projection of nonautonomous slave dynamics. They occupy a thin layer that we approximate by invariant curve interval (see text for details).

Image of FIG. 6.
FIG. 6.

(a) Spiking phase bifurcation diagram for normalized phase, , mod1, depending on interaction strength . For fixed the dots show map attractors. (b), (c) Two enlarged regions of the diagram. Parameter values: , , .

Image of FIG. 7.
FIG. 7.

PMC and corresponding map attractors shown by dots for different values of . Parameter values: , , . (a) Stable fixed point near saddle-node bifurcation, . (b) Intermittency attractor emerged from the saddle-node bifurcation, . (c) Stable periodic window with 6:5 spike locking ratio, . (d) Intermittency attractor near period doubling bifurcation, . (e) Stable fixed point corresponding to 2:1 spike locking mode, . (f) Map attractor for large number of PMC discontinuities, .

Image of FIG. 8.
FIG. 8.

Response time series for different values of . (a) . (b) . (c) .

Image of FIG. 9.
FIG. 9.

Unidirectional coupling circuit.

Image of FIG. 10.
FIG. 10.

Experimental spiking phase maps. (a) Stable fixed point corresponding to 1:1 spike frequency locking for . (b) Intermittency behavior for . (c) Intermittency with unstable oscillatory fixed point for . Phase map corresponding to rare spike response for .

Image of FIG. 11.
FIG. 11.

Bifurcation diagram (Fig. 5 ) for digital variable .

Image of FIG. 12.
FIG. 12.

(a) A chaotic route for digital variable in -plane. (b) Digital sequence . Parameter values: , , , .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spiking dynamics of interacting oscillatory neurons