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
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
| Original language | English |
|---|---|
| Pages (from-to) | 16-19 |
| Number of pages | 4 |
| Journal | Chaos, Solitons & Fractals |
| Volume | 99 |
| Early online date | 27 Mar 2017 |
| DOIs | |
| Publication status | Published - Jun 2017 |
Bibliographical note
We would like to thank the partial support of this work by the Brazilian agencies FAPESP (processes: 2011/19296-1 and 2013/26598-0, CNPq and CAPES. MSB acknowledges EPSRC Ref. EP/I032606/1.Keywords
- fractal boundaries
- parameters space
- Complex Periodic windows