Synchronization in a market model with time delays

TL;DR

This paper investigates synchronization phenomena in a financial market model with coupled delay-differential equations, analyzing bifurcations, amplitude death, phase locking, and limit cycles through analytical and numerical methods.

Contribution

It introduces a detailed analysis of market synchronization in delay systems, including bifurcation diagrams and extension to multi-asset models with N>2.

Findings

Identification of bifurcation regions leading to synchronization or amplitude death

Demonstration of limit cycle persistence in multi-asset models

Analytical and numerical characterization of collective dynamics

Abstract

We examine a system of N=2 coupled non-linear delay-differential equations representing financial market dynamics. In such time delay systems, coupled oscillations have been derived. We linearize the system for small time delays and study its collective dynamics. Using analytical and numerical solutions, we obtain the bifurcation diagrams and analyze the corresponding regions of amplitude death, phase locking, limit cycles and market synchronization in terms of the system frequency-like parameters and time delays. We further numerically explore higher order systems with N>2, and demonstrate that limit cycles can be maintained for coupled N-asset models with appropriate parameterization.