Zero-Hopf bifurcation analysis in delayed differential equations with two delays

Abstract

In this manuscript, we provide a framework for zero-Hopf singularity for a general two dimensional system with two delays. The distribution of the eigenvalues for the linearized system at an equilibrium point is studied in detail. Explicit conditions for the system to undergo a zero-Hopf bifurcation are established and the corresponding normal form up to the third order terms is derived. Our theoretical results are applied to a Kaldor–Kalecki model of business cycles.