MODIFIED VAN DER POL OSCILLATOR MODEL FOR PROFIT-TAKING AND RE-ENTRY DYNAMICS IN STOCK MARKETS

Abstract

Over the years and building upon the existing literature, it becomes evident that while various models exist to explain and predict investor behaviour and market dynamics, there is a lack of research specifically applying the Van der Pol oscillator to model the endogenous cyclicality of aggregate profit-taking and re-entry dynamics in stock markets. Existing models may not adequately capture the self-sustaining nature and nonlinear characteristics of these cycles. This study aims to fill this gap by investigating the feasibility and effectiveness of using the Van der Pol oscillator to model these key aspects of investor behaviour. The modified Van der Pol oscillator model developed in this paper provides a quantitative framework for modelling cyclical investor behaviour, that involves profit-taking and re-entry dynamics in stock markets. The limit cycle behaviour of this model naturally describes recurring bull/bear phases while the nonlinear damping captures asymmetric investor behaviour (greed vs. fear).  By calibrating the model to relevant market data and analysing its dynamic properties, this paper seeks to provide a novel perspective on the underlying mechanisms driving the cyclical ebb and flow of investor participation in stock markets.