Abstract

CASAS-GARCIA, K. et al. Asymptotically stable equilibrium points in new chaotic systems. Nova scientia [online]. 2016, vol.8, n.16, pp.41-58. ISSN 2007-0705.

In this paper ten new chaotic nonlinear autonomous systems are presented. These systems were found by using the Monte Carlo method and they characterized by having one of their equilibrium points asymptotically stable. These new systems does not present chaos in the sense of Shilnikov, but their bifurcation diagrams show a period-doubling route towards chaos. Kaplan- Yorke dimensions were also calculated, which is fractional order enclosed in a range of 2-3.

Keywords : Chaotic systems; asymptotically stable equilibrium; non-existence of Shilnikov chaos; Lyapunov exponents.