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Burst synchronization transitions in a neuronal network of subnetworks
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10.1063/1.3559136
/content/aip/journal/chaos/21/1/10.1063/1.3559136
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/1/10.1063/1.3559136
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Schematic presentation of the considered network architecture. The whole network consists of subnetworks, each containing neurons. Within each subnetwork, every neuron is connected to its six nearest neighbors, and there are seven connections amongst neurons from different subnetworks.

Image of FIG. 2.
FIG. 2.

Two burst synchronization transitions are induced by the random link probability . The spatiotemporal patterns shown in (a) , (c) , and (e) are burst synchronized patterns, while the spatiotemporal patterns shown in (b) and (d) are the transition ones. Here , and . The vertical and horizontal of the spatiotemporal patterns indicates time and neuron index, respectively. The color profile is linear, black depicting and white , .

Image of FIG. 3.
FIG. 3.

Variation of the order parameter with respect to for and .

Image of FIG. 4.
FIG. 4.

Two burst synchronization transitions are induced by the intercoupling strength . The spatiotemporal patterns shown in (a) , (c) , and (e) are burst synchronized patterns, while the spatiotemporal patterns shown in (b) and (d) are the transition ones. Here , and .

Image of FIG. 5.
FIG. 5.

Variation of the order parameter with respect to for and .

Image of FIG. 6.
FIG. 6.

Two burst synchronization transitions are induced by the intracoupling strength . The spatiotemporal patterns shown in (a) , (c) , and (e) are burst synchronized patterns, while the spatiotemporal patterns shown in (b) and (d) are the transition ones. Here , and .

Image of FIG. 7.
FIG. 7.

Variation of the order parameter with respect to for and .

Image of FIG. 8.
FIG. 8.

Dependence of the order parameter on (a) and with , and (b) and with . Burst synchronization transitions induced by the intra- and intercoupling strengths and the probability are clearly visible from these two figures.

Image of FIG. 9.
FIG. 9.

Variation of the order parameter with respect to (a) for ; (b) for ; and (c) for . The network size is and the number of subnetworks is .

Image of FIG. 10.
FIG. 10.

Variation of the order parameter with respect to for , where .

Image of FIG. 11.
FIG. 11.

Two burst synchronization transitions are induced by the number of subnetworks . The spatiotemporal patterns shown by (a) , (c) , and (e) are burst synchronized patterns, while the spatiotemporal patterns shown by (b) and (d) are the transition ones. Here , and .

Image of FIG. 12.
FIG. 12.

(Color online) (Left panels) Time series of membrane potential for one typical neuron with (a) , (c) , and (e) , respectively. (Right panels) The corresponding trajectories of the left panels for a randomly chosen neuron. The other parameters are taken the same as in Fig. 2.

Image of FIG. 13.
FIG. 13.

Burst synchronization transitions are induced by the intracoupling strength in a chemically coupled neuronal network with . Burst synchronization patterns transferring from (a) to (c) is via spike-adding, while burst synchronization patterns transferring form (c) to (e) is via change of bursting type. The spatiotemporal patterns shown by (b) and (d) are transition ones. Here , and .

Image of FIG. 14.
FIG. 14.

Burst synchronization transition is induced by the intercoupling strength in a chemically coupled neuronal network with . (a) , (b) , and (c) . This burst synchronization transition happens through the change of bursting type. Here , and .

Image of FIG. 15.
FIG. 15.

Burst synchronization transition is induced by in a chemically coupled neuronal network with . (a) , (b) , and (c) . This burst synchronization transition happens through the change of spiking number per burst. Here , and .

Image of FIG. 16.
FIG. 16.

(Color online) Phase portraits of a single neuron for chemical synapses. From (a) to (c), , and , respectively. Spike-adding and transition to FH bursting are both observed. Here , and .

Image of FIG. 17.
FIG. 17.

(Color online) Phase portraits of a single neuron for chemical synapses. (i) Transition from FHC bursting to FH bursting is observed as increasing from (a) to (b) , where and . (ii) Spike-adding is observed as increases from (c) to (d) , where , and .

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/content/aip/journal/chaos/21/1/10.1063/1.3559136
2011-03-29
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Burst synchronization transitions in a neuronal network of subnetworks
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/1/10.1063/1.3559136
10.1063/1.3559136
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