Echo state wavelet network with small-world scale-free characteristics

For adaptability problems of the reservoir, a composite echo state network (CESN) model was proposed. The small-world scale-free evolving state reservoir was constructed based on the incremental growth rules to relax the restriction for the spectral radius of the state reservoir. Moreover, discrete wavelet function was used as the activation function of neurons in CESN. The Symlets wavelet function was substituted for the fractional S-function of reservoir neurons, its dilation and translation features contributed to expanding the state space of dynamic reservoir. CESN can be applied to solve some approximation problems of nonlinear time series, which are the NARMA system, Henon map and the CO₂ concentration prediction. The experiment results show that CESN is able to significantly outperform the ESN with injected Symlets wavelet (S-ESN) and scale-free highly clustered echo state network (SHESN) in approximating highly complex nonlinear dynamics.