Nonlinear dynamics and bifurcation analysis in two models of sustainable development

Abstract

We show in this document two mathematical models of development. Namely, we state two systems of nonlinear differential equations with state variables which regard to ecosystem, social and economic dimensions. We analyze nonlinear dynamics through bifurcation theory and state space simulations. Complex nonlinear systems including variables from ecosystem, social and economic dimensions show that, depending on the parameter values and initial conditions, different patterns can be obtained. Some of these patterns are related to fast decay of the exhaustible resources. Thus, also fast sustainable actions must be taken into account to prevent ecological disasters.