Regimes and mechanisms of transient amplification in abstract and biological neural networks
Fig 2
Eigenspectra and dynamics of the corresponding networks.
A–D, Four cases of eigenspectra and dynamics of the corresponding network of size N = 200. In each panel, clockwise: The spectrum; linear dynamics; non-linear dynamics; the logarithm of the maximum norm of the firing rate per initial condition. The same initial condition that elicits the maximum norm is used for both linear and non-linear dynamics. Pink dotted line indicates the percentage of conditions whose norm is amplified by at least 50%. The feedforward structure is taken from a stability-optimised circuit [8] and its Frobenius norm is fixed to 75. Real and imaginary parts follow an uniform distribution with diameters dim and dre, respectively. A, When dim = dre = 10, only 1% (2 out of 200) of the conditions are slightly amplified. B, When dim = 10 and dre = 1, the system is capable of more amplification. C, Here, dim = 1 and dre = 10, surprisingly creating more amplification compared to the case shown in panel A. D, When dim = dre = 1, the system amplifies almost half of the initial conditions. The dynamics, given an initial condition of norm 1, reach the value of ∼ 105 Hz in the linear case and consequently long-lasting dynamics in the non-linear case.