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Relating the sequential dynamics of excitatory neural networks to synaptic cellular automata
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10.1063/1.3657384
/content/aip/journal/chaos/21/4/10.1063/1.3657384
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/4/10.1063/1.3657384

Figures

Image of FIG. 1.
FIG. 1.

(Color online) The phase portraits of the system (9) which correspond respectively to (a) ; (b) ; (c) ; and (d) α > α *. The other parameters satisfy the conditions (12). The dashed curves on figures are nullclines.

Image of FIG. 2.
FIG. 2.

(Color online) The fragments of trajectories formed in the coupling subsystem of Eqs. (3) and (4) as a result of the processes of its activation and inactivation for (a) weak and (b) strong stimulations. In both cases the stimulation χi (t) represents a sequence of three square pulses with the same amplitude and duration. The amplitude of pulses equals 1; the durations are (a) 3 and (b) 6. The parameters are given by Eq. (14).

Image of FIG. 3.
FIG. 3.

Waveforms of the synaptic variable in the case of (a) slow and (b) fast synaptic responses. They correspond to trajectories Tr depicted on Figs. 2(a) and 2(b), respectively.

Image of FIG. 4.
FIG. 4.

(Color online) (a) Bifurcation diagram and (b) a trajectory in the non-autonomous phase space. The parameters are given by Eq. (16).

Image of FIG. 5.
FIG. 5.

(Color online) (a) The architecture of neural network and (b) elementary clusters of the network. Here ni and si signify the neurons and synapses, respectively.

Image of FIG. 6.
FIG. 6.

(Color online) Graph of connections G corresponding to neural network presented in Fig. 5(a).

Image of FIG. 7.
FIG. 7.

(a) A part of the basin of the fixed point A 0 and (b) a part of the basin of the periodic attractor A 1.

Image of FIG. 8.
FIG. 8.

Unfolding for the periodic attractor A 1 of CA.

Image of FIG. 9.
FIG. 9.

(Color) Unfolding and realizations for established regimes in the network: (a) - unfolding; (b) - realizations for synapses; and (c) - realizations for neurons. The parameters are defined by Eqs. (14) and (16). The values of threshold constants are: θ 13 = θ 23 = θ 32 = −0.03, θ 34 = 0.0, θ 41 = −0.02. All other thresholds are set to 2.

Tables

Generic image for table
Table I.

Rules of the synaptic CA.

Generic image for table
Table II.

The rules .

Generic image for table
Table III.

The rules .

Generic image for table
Table IV.

The rules .

Generic image for table
Table V.

The rules .

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/content/aip/journal/chaos/21/4/10.1063/1.3657384
2011-11-16
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Relating the sequential dynamics of excitatory neural networks to synaptic cellular automata
http://aip.metastore.ingenta.com/content/aip/journal/chaos/21/4/10.1063/1.3657384
10.1063/1.3657384
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