Synthesis method of neural oscillators by network learning

In the biological systems there are numerous examples of autonomously generated periodic activities. This paper proposes a synthesis method of neural oscillators by neural network learning. The problem is formulated as determining the weights of the synaptic connections of neural networks such that, the neural networks generate desired autonomous limit cycles. We introduce a new architecture of neural networks, hybrid recurrent neural networks, in order to enhance the capability of implementing neural oscillators. In order to generate autonomous limit cycles in the neural networks we make use of the bifurcation theory. Efficient learning methods for synthesizing neural oscillators with desired limit cycles are derived. Synthesis examples are also presented to demonstrate the applicability and performance of the proposed method.