Low-dimensional chaos induced by frustration in a non-monotonic system

TL;DR

This paper introduces a new mechanism called frustration-induced chaos in a non-monotonic associative memory model, showing that frustration leads to low-dimensional chaos at the macroscopic level through analytical derivation and bifurcation analysis.

Contribution

It derives exact macroscopic equations from microscopic dynamics and demonstrates that frustration is essential for chaos in this system.

Findings

Chaos is low-dimensional when frustration is present.

Chaos does not occur without frustration.

Bifurcation diagrams reveal the role of frustration in chaos emergence.

Abstract

We report a novel mechanism for the occurrence of chaos at the macroscopic level induced by the frustration of interaction, namely frustration-induced chaos, in a non-monotonic sequential associative memory model. We succeed in deriving exact macroscopic dynamical equations from the microscopic dynamics in the case of the thermodynamic limit and prove that two order parameters dominate this large-degree-of-freedom system. Two-parameter bifurcation diagrams are obtained from the order-parameter equations. Then we analytically show that the chaos is low-dimensional at the macroscopic level when the system has some degree of frustration, but that the chaos definitely does not occur without the frustration.