From local bifurcations to global dynamics : hopf systems from the applied perspective

This chapter consists of four sections. Section 5.1 reiterates with the Hopf bifurcation theorem. Section 5.2 provides two specific systems that generate chaotic motions by means of numerical simulations. Section 5.3 explains Shilnikov’s theorem. Finally, Sect. 5.4 treats the emergence of chaos in the nonlinear system of the delay-differential equations. To link the chaos theory to economic modelling, at the end of each section, we include simple examples of applications to economics.