Oscillatory networks with Hebbian matrix of connections
The systems of symmetrically coupled limit cycle oscillators admit the design of recurrent associative memory networks with Hebbian matrix of connections. Unlike the similar neural networks this matrix proved to be the complex-valued Hermitian one with nonzero diagonal. In the case of strong interaction in oscillatory system the memory vectors of the network are slightly perturbed properly normalized eigenvectors of matrix of connections. They can be calculated by perturbation method on the appropriate small parameter. The self-consistent analysis of dynamical system fixed points in the case of homogeneously all-to-all connected oscillators is presented. It is proved that for positive values of connection strength only a single memory vector can be stored. Some questions concerning the ”extraneous” memory of the networks are discussed.
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