Zero–Hopf bifurcation analysis of a Kaldor–Kalecki model of business cycle with delay

The zero–Hopf singularity of a Kaldor–Kalecki model of business cycle with delay in both the gross product and the capital stock is investigated. By computing the normal forms for the system, the bifurcation diagrams such as saddle-node, pitch-fork, and Hopf bifurcations are obtained. A major obstacle is to solve singular linear systems when the third order terms in the normal form are computed. Some examples are presented to confirm the theoretical results.