Dynamics of a Delayed Kaldor-Kalecki Model of Mutually Linked Economies

The Kaldor-Kalecki business cycle model unifies the concept of non-linearity of the investment function of Kaldor and the concept of investment lag of Kalecki. Recently, the influence of a global economy on a local economy was investigated using delayed Kaldor-Kalecki models that are coupled unidirectionally. In this work, we proposed and analyzed a business cycle model of two mutually linked economies described using bidirectionally coupled Kaldor-Kalecki models. For the case of comparable economies, we obtain an equivariant system. This symmetry property is then used to classify the Hopf bifurcations and consequently determine the different types of oscillatory patterns that can occur in the proposed business cycle model. Our result is further expanded using numerical continuation which detected the occurrence of various limit-cycle bifurcations including period-doubling and torus bifurcations which give rise to different kinds of oscillations. This diversity in oscillatory behavior is crucial to better depict economic cycles.