Encoding and Replay of Dynamic Attractors with Multiple Frequencies: Analysis of a STDP Based Learning Rule

After learning, each encoded oscillatory spatio-temporal pattern who satisfy the stability condition forms a dynamical attractor, such that, when the state of the system falls in the basin of attraction of one such dynamical attractor, it is recovered with the same encoded phase relationship among units. Here we extend the analysis introduced in our previous work, to the case of distributed frequencies, and we study the relation between stability of multiple frequencies and the shape of the learning window. The stability of the dynamical attractors play a critical role. We show that imprinting into the network a spatio-temporal pattern with a new frequency of oscillation can destroy the stability of patterns encoded with different frequency of oscillation. The system is studied both with numerical simulations, and analytically in terms of order parameters when a finite number of dynamic attractors are encoded into the network in the thermodynamic limit.