Bifurcation analysis in an associative memory model

TL;DR

This paper analyzes bifurcation phenomena in a finite-temperature stochastic associative memory model, revealing how temperature influences chaos and attractor coexistence, extending previous zero-temperature chaos studies.

Contribution

It introduces a bifurcation analysis at finite temperature for a non-monotonic associative memory model, deriving order-parameter equations from microscopic dynamics.

Findings

Temperature reduces chaos in the model.

Coexistence of multiple attractors emerges at finite temperature.

Bifurcation diagrams illustrate the effects of temperature on system dynamics.

Abstract

We previously reported the chaos induced by the frustration of interaction in a non-monotonic sequential associative memory model, and showed the chaotic behaviors at absolute zero. We have now analyzed bifurcation in a stochastic system, namely a finite-temperature model of the non-monotonic sequential associative memory model. We derived order-parameter equations from the stochastic microscopic equations. Two-parameter bifurcation diagrams obtained from those equations show the coexistence of attractors, which do not appear at absolute zero, and the disappearance of chaos due to the temperature effect.