Non-linear and non-smooth dynamics in a sustainable development system

Abstract

This paper presents the dynamic interaction between natural resource and population, and also introduce technological progress as an extra dynamic equation. Hopf, saddlenode, and two-parameter bifurcation were found in the planar system, and chaotic behaviour appeared in the 3D system. Nonsmooth phenomena such as sliding and stable pseudo equilibrium appeared when smooth systems were replaced by non-smooth system.