The Emergence of Bull and Bear Dynamics in a Nonlinear Model of Interacting Markets

We develop a three-dimensional nonlinear dynamic model in which the stock markets of two countries are linked through the foreign exchange market. Connections are due to the trading activity of heterogeneous speculators. Using analytical and numerical tools, we seek to explore how the coupling of the markets may affect the emergence of bull and bear market dynamics. The dimension of the model can be reduced by restricting investors' trading activity, which enables the dynamic analysis to be performed stepwise, from low-dimensional cases up to the full three-dimensional model. In our paper we focus mainly on the dynamics of the one- and two- dimensional cases, with numerical experiments and some analytical results, and also show that the main features persist in the three-dimensional model.