Lyapunov functions for rotor neural networks

Research output: Contribution to journalConference articlepeer-review


The state of a rotor neuron is constrained to live on the surface of a sphere in Rn. A rotor neural network is used to minimize an arbitrary cost function with respect to these 'spherical' states. One practical example of such a situation is optimal charge distribution on a sphere in electromagnetism. In this paper, I show that if the cost function is quadratic in the neuron states, the synchronous, iterated-map algorithm used to find the fixed-points of the network has a Lyapunov function. I also propose a continuous-time dynamical system for finding the fixed-points that is valid for any cost function. Moreover, I show that this continuous-time dynamics has a Lyapunov function. Finally, I show that a similar continuous-time algorithm and a similar Lyapunov function can be used for solving fixed-point equations more general than those of rotor neural networks.

Original languageBritish English
Pages (from-to)3355-3356
Number of pages2
JournalProceedings of the American Control Conference
StatePublished - 1994
EventProceedings of the 1994 American Control Conference. Part 1 (of 3) - Baltimore, MD, USA
Duration: 29 Jun 19941 Jul 1994


Dive into the research topics of 'Lyapunov functions for rotor neural networks'. Together they form a unique fingerprint.

Cite this