Synchronization in a market model with time delays

ArXiv ID: 2405.00046 “View on arXiv”

Authors: Unknown

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.

Keywords: Coupled Non-linear Delay-Differential Equations, Time Delay Systems, Bifurcation Analysis, Amplitude Death, Market Synchronization, Multi-Asset

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats
• Why: The paper is dominated by advanced mathematical analysis involving delay-differential equations, linearization, characteristic equations, and bifurcation theory, but it contains no real-world data, backtests, or implementation details for trading.

  flowchart TD
    A["Research Goal:<br>Analyze synchronization in coupled<br>non-linear delay-differential market models"] --> B["Methodology:<br>Linearization, Analytical &<br>Numerical Solutions"]
    B --> C["Data/Input:<br>System of N=2 coupled<br>DDEs & time delay parameters"]
    C --> D["Computational Process:<br>Bifurcation Analysis &<br>Numerical Simulations"]
    D --> E["Key Outcomes:<br>Amplitude Death, Phase Locking,<br>Limit Cycles, Market Synchronization"]
    E --> F["Extension:<br>N>2 assets showing sustained<br>limit cycles & multi-asset dynamics"]