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Optimal system size for complex dynamics in random neural networks near criticality
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View: Figures


Image of FIG. 1.
FIG. 1.

Illustration of the various sample time-series of system (1) with a given choice of the disorder parameter  = 1 and system size  = 40. Each figure corresponds to a random choice of the connectivity matrix and random initial conditions.

Image of FIG. 2.
FIG. 2.

Numerical estimation of the probability of observing (a) spontaneous activity, (b) limit cycles, (c) chaotic trajectories, and (d) chaotic attractor given spontaneous activity, as a function of and for different values of {0.95,0.96,0.97,0.98,0.99,1}. For each matrix size and each value of  1, 5.104 realizations of the random matrix have been analyzed and the sigmoid function used was tanh( ). Standard deviations errors are smaller than the points, therefore not shown. Numerical estimations of the maximal Lyapunov exponent were performed after cutting a first period of transient dynamics.

Image of FIG. 3.
FIG. 3.

Real Ginibre ensemble: numerical estimation of and A total of 5 × 105 Monte-Carlo runs were computed for each different matrix sizes and value of .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Optimal system size for complex dynamics in random neural networks near criticality