6533b7dcfe1ef96bd1272cae
RESEARCH PRODUCT
Massive evaluation and analysis of Poincar�� recurrences on grids of initial data: a tool to map chaotic diffusion
Guillaume RollinA. V. MelnikovIvan I. ShevchenkoJosé Lagessubject
Dynamical systems theoryComputer scienceChaoticGeneral Physics and AstronomyFOS: Physical sciencesLyapunov exponent01 natural sciences010305 fluids & plasmasHamiltonian systemsymbols.namesakeSimple (abstract algebra)0103 physical sciencesApplied mathematicsDiffusion (business)010306 general physicsInstrumentation and Methods for Astrophysics (astro-ph.IM)ComputingMilieux_MISCELLANEOUSEarth and Planetary Astrophysics (astro-ph.EP)Numerical analysisNonlinear Sciences - Chaotic DynamicsHardware and ArchitectureBounded functionsymbolsChaotic Dynamics (nlin.CD)Astrophysics - Instrumentation and Methods for Astrophysics[PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph]Astrophysics - Earth and Planetary Astrophysicsdescription
We present a novel numerical method aimed to characterize global behaviour, in particular chaotic diffusion, in dynamical systems. It is based on an analysis of the Poincar\'e recurrence statistics on massive grids of initial data or values of parameters. We concentrate on Hamiltonian systems, featuring the method separately for the cases of bounded and non-bounded phase spaces. The embodiments of the method in each of the cases are specific. We compare the performances of the proposed Poincar\'e recurrence method (PRM) and the custom Lyapunov exponent (LE) methods and show that they expose the global dynamics almost identically. However, a major advantage of the new method over the known global numerical tools, such as LE, FLI, MEGNO, and FA, is that it allows one to construct, in some approximation, charts of local diffusion timescales. Moreover, it is algorithmically simple and straightforward to apply.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2020-01-01 |