This is a past event
Interdisciplinary seminar by Dr Matheus Rohim Sales (São Paulo State University and the University of Essex)
Topic: Recurrence time entropy: A chaotic indicator for weakly chaotic systems
Description: In two-dimensional, area-preserving mappings with hierarchical phase space, chaotic orbits can spend an arbitrarily long time around stability islands, during which they behave similarly to quasiperiodic orbits. This phenomenon is called stickiness, and it is due to the presence of partial barriers to the transport around the hierarchical levels of islands-around-islands. The stickiness affects the convergence of the Lyapunov exponents, making the task of characterizing the dynamics more difficult, especially when only short time series are known. Due to the intrinsic property of dynamical systems that quasiperiodic orbits can have at most three different return times (Slater’s theorem), which is the time needed for the orbit to return to a given region along the orbit, in this talk, we discuss the use of the recurrence time entropy (RTE) (estimated from the recurrence plots) to characterize the dynamics of nonlinear systems. We find that the RTE is an alternative way of detecting chaotic orbits and sticky regions. Furthermore, the finite-time RTE distribution is multi-modal when sticky regions are present in the phase space, and each mode corresponds to a different hierarchical level in the islands-around-islands structure embedded in the chaotic sea.
- Speaker
- Dr Matheus Rolim Sales
- Venue
- Meston 311