Differ Equ Dyn Syst (Jan&Apr 2013) 21(1&2):173–184 DOI 10.1007/s12591-012-0138-2 ORIGINAL RESEARCH Smooth and Filippov Models of Sustainable Development: Bifurcations and Numerical Computations Jorge A. Amador · Gerard Olivar · Fabiola Angulo Published online: 29 September 2012 © Foundation for Scientific Research and Technological Innovation 2012 Abstract This paper presents a system of ordinary differential equations in order to explain each one of the sustainable development dimensions (resource, economy and social growth) and their dependance with population growth. Simulations show that system is highly depen- dant on social and technological parameters, which induce different types of bifurcations. Hopf, saddle-node, homoclinic, codimension-two bifurcation points and chaotic behavior appeared in the system. Non-smooth such as sliding and stable pseudo equilibrium are also present when continuous systems are replaced by Fillipov systems. Analysis conclude that for a sustainable scheme, several sustainability actions must be introduced in the system in order to keep non-trivial equilibrium or stationary oscillations among the dimensions. Keywords Sustainability · Bifurcation · Filippov Introduction The concept of sustainable development implies worldwide responsibility and shift to more sustainable lifestyles and patterns of consumption and production in order to obtain harmony among society, economy, and nature. This concept includes current and future global environ- mental concerns and must consider the role of ethics in determining choices affecting local and global environmental conditions. For example, the way science and new technologies are This paper has been presented during 11th Conference on Dynamical Systems—Theory and Applications. J. A. Amador · G. Olivar (B ) · F. Angulo Departamento de Ingeniería Eléctrica, Electrónica y Computación, Percepción y Control Inteligente, Facultad de Ingeniería y Arquitectura, Universidad Nacional de Colombia, Sede Manizales, Bloque Q, Campus La Nubia, Manizales 170003, Colombia e-mail: golivart@unal.edu.co J. A. Amador e-mail: jaamadorm@unal.edu.co F. Angulo e-mail: fangulog@unal.edu.co 123