Author’s reply to: Comments on “Asymptotically stable equilibrium points in new chaotic systems”

Abstract

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.

Keywords

• chaotic systems
• asymptotically stable equilibrium
• non-existence of Shilnikov chaos
• Lyapunov exponents