SO(2)-Networks as Neural Oscillators
Using discrete-time dynamics of a two neuron networkw ith recurrent connectivity it is shown that for specific parameter configurations the output signals of neurons can be of almost sinusoidal shape. These networks live near the Sacker-Neimark bifurcation set, and are termed SO(2)-networks, because their weight matrices correspond to rotations in the plane. The discretized sinus-shaped waveform is due to the existence of quasi-periodic attractors. It is shown that the frequency of the oscillators can be controlled by only one parameter. Signals from the neurons have a phase shift of Π/2 and may be useful for various kinds of applications; for instance controlling the gait of legged robots.
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- 2.Haschke, R., Steil, J.J., and Ritter, H. (2001), Controlling oscillatory behaviour of a two neuron recurrent neural networkus ing inputs, in: G. Dorffner, H. Bischof, K. Hornik ( Eds.): Artificial Neural Networks-ICANN 2001, International Conference Vienna, Austria, August 21–25, 2001, Proceedings. LNCS 2130, Springer Verlag, Berlin, p. 1109 ff.CrossRefGoogle Scholar