En este trabajo se presentan 10 nuevos sistemas autónomos no lineales caóticos simples. Estos sistemas se encontraron utilizando el método Monte Carlo y tienen la característica de tener uno de sus puntos de equilibrio asintóticamente estables. Estos nuevos sistemas no tienen caos en el sentido de Shilnikov, pero sus diagramas de bifurcación muestran una ruta de periodo doble hacia el caos. Se calculó también la dimensión de Kaplan-Yorke, dando como resultado en un rango de 2-3.

Based on a wider systematic search on a family of 3-dimensional systems with quadratic nonlinearities, three new simple chaotic systems were found. One of them has the unusual feature of having a stable equilibrium point, and it is the simplest one of other chaotic flows with this property. The others have some interesting special properties.

Since theorem 1 of (Elhadj and Sprott, 2012) is incorrect, some of the systems found in the article (Casas-García et al. 2016) may have homoclinic or heteroclinic orbits and may seem chaos in the Shilnikov sense. However, the fundamental contribution of our paper was to find ten simple, three-dimensional dynamic systems with non-linear quadratic terms that have an asymptotically stable equilibrium point and are chaotic, which was achieved. These were obtained using the Monte Carlo method applied specifically for the search of these systems.