Sensitive dependence on parameters of continuous-time nonlinear dynamical systems. (June 2017)

• Record Type: Journal Article
• Authors: Medeiros, E.S.; Caldas, I.L.; Baptista, M.S.
• Is Part Of: Chaos, solitons and fractals. Volume 99(2017)
• Page Start: 16
• Page End: 19
• Publication Date: 2017-06
• Subjects: Fractal boundaries -- Parameters space -- Complex periodic windows; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2017.03.043
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: The sensitive dependence of periodicity and chaos on parameters is investigated for three-dimensional nonlinear dynamical systems. Previous works have found that noninvertible low-dimensional maps present power-law exponents relating the uncertainty between periodicity and chaos to the precision on the system parameters. Furthermore, the values obtained for these exponents have been conjectured to be universal in these maps. However, confirmation of the observed exponent values in continuous-time systems remain an open question. In this work, we show that one of these exponents can also be found in different classes of three-dimensional continuous-time dynamical systems, suggesting that the sensitive dependence on parameters of deterministic nonlinear dynamical systems is typical.