Asset Price Dynamics in a Chartist‐Fundamentalist Model with Time Delays: A Bifurcation Analysis

This paper studies the dynamic behavior of asset prices using a chartist‐fundamentalist model with two speculative markets. To this effect, we employ a differential system with delays à la Dibeh (2007) to describe the price dynamics and we assume that the two markets are coupled via diffusive coupling terms. We study two different time delay cases, namely, when both markets experience the same time delay and when the time delay is different across markets. First, we theoretically determine that the equilibrium exists and investigate its stability. Second, we establish the general conditions for the existence of local Hopf bifurcations and analyze their direction and stability. The common conclusion from both the delay scenarios we consider is that coupled speculative markets with heterogeneous agents in each, but with different price dynamics, can be synchronized through diffusive coupling. Finally, we provide some numerical illustrations to confirm our theoretical findings.