Oscillation of the Overlap Parameter in a Phase Coupled Model
Satoshi Kawaguchi · Progress of Theoretical Physics · 2002
A phase coupled oscillator neural network for associative memory is studied. The natural frequency is assumed to be distributed among several types. We use an overlap parameter in order to measure the ability of the retrieval system. When there are higher frequency neurons with sufficiently large population fraction, the system cannot converge to an equilibrium state, and the overlap oscillates. This periodic oscillation is destabilized to quasi-periodic or chaotic oscillation through the period-doubling route as the range of the natural frequency increases. In this research, we numerically investigate the oscillation of the overlap. We find that the population whose frequency is distributed around zero remains a non-zero fixed value of the overlap. On the other hand, the other groups with higher frequencies contribute to the oscillatory components. The mean value of the oscillatory overlap determined using the modified SCSNA well agrees in case of periodic oscillation with small amplitude. However, it is difficult to evaluate this value for the quasi-periodic and chaotic oscillation, as the overlap obtained with the time average is time dependent. We discuss the dependences of the overlap oscillation and its phase diagram on the natural frequency distributions, and refer to the limitations of the existing theories for the equilibrium state.