Abstract. The concept of sustainable development implies worldwide responsibility and shift to a more sustainable lifestyles and patterns of consumption and production to obtain the harmony among society, economy, and nature. Nowadays, sustainable development is extensively described and studied, but very few works are dedicated to mathematical modelling techniques and numerical simulations. This work deals with some systems of ordinary differential equations in order to explain each one of the sustainable development dimensions (resources, economy, and social growth) and their dependence with population growth. As a result non-linear phenomena such as bifurcations and chaotic behavior may appear and help to explain some sustainability conditions revealing new features of sustainable development dynamics. Non-smooth phenomena such as sliding may appear when discontinuities are introduced into the system turning them into Filippov systems.