Emerging attractors and the transition from dissipative to conservative dynamics

Christian S Rodrigues, Alessandro P S de Moura, Celso Grebogi

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The topological structure of basin boundaries plays a fundamental role in the sensitivity to the final state in chaotic dynamical systems. Herewith we present a study on the dynamics of dissipative systems close to the Hamiltonian limit, emphasizing the increasing number of periodic attractors, and on the structural changes in their basin boundaries as the dissipation approaches zero. We show numerically that a power law with nontrivial exponent describes the growth of the total number of periodic attractors as the damping is decreased. We also establish that for small scales the dynamics is governed by effective dynamical invariants, whose measure depends not only on the region of the phase space but also on the scale under consideration. Therefore, our results show that the concept of effective invariants is also relevant for dissipative systems.

Original languageEnglish
Article number026205
Number of pages8
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Volume80
Issue number2
DOIs
Publication statusPublished - Aug 2009

Fingerprint

Dissipative Systems
Attractor
emerging
Chaotic Dynamical Systems
Structural Change
Topological Structure
Invariant Measure
dynamical systems
Dissipation
Phase Space
Damping
Power Law
dissipation
damping
Exponent
exponents
Invariant
sensitivity
Zero
Concepts

Keywords

  • chaos
  • fractals
  • topology
  • basin boundaries
  • complexity
  • dimension
  • systems
  • cells

Cite this

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KW - complexity

KW - dimension

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KW - cells

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