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Related Experiment Videos

Bubbling and on-off intermittency in bailout embeddings.

Julyan H E Cartwright1, Marcelo O Magnasco, Oreste Piro

  • 1Laboratorio de Estudios Cristalográficos, CSIC, E-18071 Granada, Spain. julyan@lec.ugr.es

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 26, 2003
PubMed
Summary

This study links Hamiltonian system dynamics to bubbling and blowout bifurcations. It reveals how embedded Hamiltonian systems exhibit transient intermittency and noise-induced phase space avoidance, termed Hamiltonian bubbling.

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Area of Science:

  • Dynamical Systems Theory
  • Chaos Theory
  • Mathematical Physics

Background:

  • Bubbling and blowout bifurcations are critical phenomena in dynamical systems, often observed in systems with invariant manifolds.
  • These bifurcations lead to sudden changes in system behavior, such as intermittent bursts or complete state divergence.
  • Hamiltonian systems, governed by specific conservation laws, present unique dynamical properties.

Purpose of the Study:

  • To establish a conceptual link between bailout embeddings of Hamiltonian systems and the dynamics of bubbling and blowout bifurcations.
  • To identify the role of the embedded Hamiltonian system in mimicking the invariant manifold dynamics crucial for these bifurcations.
  • To characterize the specific nature of these bifurcations when occurring within a Hamiltonian context.

Main Methods:

Related Experiment Videos

  • Investigating the dynamics of bailout embeddings in Hamiltonian systems.
  • Analyzing the behavior of trajectories in relation to invariant structures.
  • Comparing the observed dynamics with established models of bubbling and blowout bifurcations.

Main Results:

  • The embedded Hamiltonian system effectively plays the role of the invariant manifold and its restricted dynamics.
  • The Hamiltonian nature of the embedded system is the defining characteristic of this bifurcation instance.
  • Trajectory detachment from the original system is identified as transient on-off intermittency.
  • Noise-induced avoidance of phase space regions is recognized as Hamiltonian bubbling.

Conclusions:

  • A clear conceptual connection exists between bailout embeddings of Hamiltonian systems and bubbling/blowout bifurcations.
  • Hamiltonian bubbling represents a novel manifestation of these bifurcations, characterized by transient intermittency and noise-induced dynamics.
  • This framework provides new insights into the behavior of complex dynamical systems with Hamiltonian components.