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Nontwist non-Hamiltonian systems.

E G Altmann¹, G Cristadoro, D Pazó

¹Max Planck Institute for the Physics of Complex Systems, Dresden, Germany. edugalt@pks.mpg.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|June 29, 2006

Summary

Nontwist phenomena, previously seen in Hamiltonian systems, also occur in time-reversible, non-Hamiltonian systems. This study explores these phenomena in collision-reconnection scenarios, revealing new routes to torus breakup.

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Area of Science:

Nonlinear dynamics
Chaos theory
Statistical mechanics

Background:

Nontwist phenomena are well-documented in Hamiltonian systems, influencing their long-term behavior.
Understanding these phenomena is crucial for predicting the stability and dynamics of complex systems.

Purpose of the Study:

To investigate the existence and characteristics of nontwist phenomena in time-reversible non-Hamiltonian systems.
To analyze the parameter space breakup diagram of the shearless torus in these systems.
To identify novel routes to torus breakup beyond traditional Hamiltonian mechanisms.

Main Methods:

Analysis of two standard collision-reconnection scenarios.
Computation of the parameter space breakup diagram for the shearless torus.
Examination of phenomena in coupled phase oscillators.
Study of dynamics in non-area-preserving maps.

Main Results:

Confirmation that nontwist phenomena are present in time-reversible non-Hamiltonian systems.
Identification of attractor onset as a significant route to torus breakup, distinct from Hamiltonian pathways.
Detailed mapping of the parameter space breakup diagram for the shearless torus.

Conclusions:

The study extends the understanding of nontwist phenomena beyond Hamiltonian systems.
New insights into torus breakup mechanisms in non-Hamiltonian dynamics are provided.
The findings have implications for diverse fields involving complex system dynamics.

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