Finding an Example of an Optimising Agent with Cyclical Behaviour

Most recent studies of dynamic macroeconomic relationships focus on models derived from optimising behaviour by economic agents. In most of these models, the eigenvalues of the associated dynamical system are real-valued and so the time-path of the system exhibits monotonic or near-monotonic behaviour. While, it is well-known that linear dynamic models with complex-valued eigenvalues exhibit the property of oscillatory dynamic behaviour, limited research has been undertaken to investigate the properties of optimising models with oscillatory behaviour. In this study, we will focus on producing an example of an optimising agent whose dynamics are characterised by complex-valued eigenvalues and who thus exhibits cyclical behaviour.