Before revision:  (i) learning the structure of a chaotic system purely from  time series, (ii) generating new streams of stimuli from a chaotic system, (iii) switching stream generation among multiple learned chaotic systems , either spontaneously or in response to external perturbations , (iv) inferring missing data from sparse observations of the chaotic system, and (v) deciphering superimposed input from different chaotic systems. Numerically, we show that these phenomena emerge naturally from a recurrent neural network of Erdos-Renyi topology in which the synaptic strengths adapt in a Hebbian-like manner. Broadly, our work blends chaotic theory and artificial neural networks to answer the long standing question of how neural systems can learn the structure underlying temporal sequences of stimuli .
After revision:  (i) learning the structure of a chaotic system purely from time series, (ii) generating new streams of stimuli from a chaotic system, (iii) switching stream generation among multiple learned chaotic systems , either spontaneously or in response to external perturbations , (iv) inferring missing data from sparse observations of the chaotic system, and (v) deciphering superimposed input from different dynamical systems. Collectively, our findings support the notion that artificial and biological neural networks can learn the structure underlying temporal sequences of stimuli .