Multiple attractors and global bifurcations in a Kaldor-type business cycle model

We consider a Kaldor-type discrete-time nonlinear business cycle model in income and capital, where investment is assumed to depend both on the difference between normal and current levels of capital stock, and on the difference between the current income and its normal level, through a nonlinear S-shaped increasing function. As usual in Kaldor business cycle models, one or three steady states exist, and the standard analysis of the local stability and bifurcations suggests that endogenous oscillations occur in the presence of only one unstable equilibrium, whereas the coexistence of three equilibria is characterized by bi-stability, the central equilibrium being on the boundary which separates the basins of the two stable ones. However, a deeper analysis of the global dynamic properties of the model in the parameter ranges where three steady states exist, reveals the existence of an attracting limit cycle surrounding the three steady states, leading to a situation of multistability, with a rich and complex dynamic structure.