Nonlinear Dynamics of Economic Cycles

Abstract

Complex dynamics of economic systems can be studied by applying the concepts and techniques of nonlinear dynamics and chaos. Some models of business cycles, such as Kaldor’s nonlinear investment-savings functions and Goodwin’s nonlinear accelerator-multiplier, can be reduced to the van der Pol equation which describes relaxation oscillations. By introducing an exogenous driver, the forced van der Pol equation can be adopted as a prototype model for complex economic dynamics. Numerical solutions of this model can elucidate the fundamental properties of complex economic systems which exhibit a wealth of nonlinear behaviors such as multistability as well as coexistence of order and chaos. Unstable periodic orbits are the skeleton of chaotic attractors in complex economic systems.