The <i>testMSEs</i> comparisons of prediction performance for four networks.

<p>The <i>testMSEs</i> comparisons of prediction performance for four networks.</p

Correlation coefficient and the responding statistical distribution of reservoir states for four networks.

<p>(a) ESN (b) C-ESN (c) LI-ESN (d) C-LI-ESN.</p

Principal component energy analysis of reservoir states for four different networks. Log PC energy: log10 of reservoir signal energies in the principal component directions. Leading PC energy: The top ten signal energies in linear scale.

<p>(a) ESN (b) C-ESN (c) LI-ESN (d) C-LI-ESN.</p

The <i>NRMSEs</i>₈₄ comparisons of prediction performance for four networks.

<p>The <i>NRMSEs</i>₈₄ comparisons of prediction performance for four networks.</p

Network output (dashed) diverges from the teaching signal (solid) when internal states become unstable (a) or divergent (b).

<p>Network output (dashed) diverges from the teaching signal (solid) when internal states become unstable (a) or divergent (b).</p

Capability of nonlinear time series prediction.

<p>The log10 testMSE of four networks vs the time delay <i>τ</i> in the Mackey-Glass system.</p

The regular echo state network model with random reservoir topology.

<p>The regular echo state network model with random reservoir topology.</p

The probability distribution of all internal states and corresponding <i>W</i>^<i>out</i> distribution of four networks during training phase.

<p>(a) ESN (b) C-ESN (c) LI-ESN (d) C-LI-ESN.</p

Teacher signal (solid) and network output (dashed) for four networks with the parameter of learning task <i>τ</i> = 30.

<p>(a) ESN (b) C-ESN (c) LI-ESN (d) C-LI-ESN.</p

Comparison of <i>testMSEs</i> of LI-ESN and C-LI-ESN for the learning task <i>τ</i> = 30.

<p>The results are obtained by 20 independent realizations.</p