Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Chaotic saddles and interior crises in a dissipative nontwist system

Journal Article · · Physical Review. E
 [1];  [2];  [3];  [4];  [5]
  1. Sao Paulo State University (UNESP) (Brazil); OSTI
  2. Sao Paulo State University (UNESP) (Brazil)
  3. Univ. of Sao Paulo (Brazil)
  4. Univ. of Sao Paulo (Brazil); Federal University of Parana, Curitiba (Brazil)
  5. Univ. of Texas, Austin, TX (United States)
+ Show Author Affiliations
Here, we consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be regular or chaotic depending on the control parameters. Chaotic attractors can undergo sudden and qualitative changes as a parameter is varied. These changes are called crises, and at an interior crisis the attractor suddenly expands. Chaotic saddles are nonattracting chaotic sets that play a fundamental role in the dynamics of nonlinear systems; they are responsible for chaotic transients, fractal basin boundaries, and chaotic scattering, and they mediate interior crises. In this work we discuss the creation of chaotic saddles in a dissipative nontwist system and the interior crises they generate. We show how the presence of two saddles increases the transient times and we analyze the phenomenon of crisis induced intermittency.
Research Organization:
Univ. of Texas, Austin, TX (United States)
Sponsoring Organization:
Coordination for the Improvement of Higher Education Personnel (CAPES); National Council for Scientific and Technological Development (CNPq); São Paulo Research Foundation (FAPESP); USDOE
Grant/Contract Number:
FG05-80ET53088
OSTI ID:
2417854
Journal Information:
Physical Review. E, Journal Name: Physical Review. E Journal Issue: 2 Vol. 107; ISSN 2470-0045
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (43)

Mathematical Methods of Classical Mechanics book January 1989
Regular and Chaotic Dynamics book January 1992
Geometrical Dissipation for Dynamical Systems journal October 2012
The dimension of chaotic attractors journal May 1983
Crises, sudden changes in chaotic attractors, and transient chaos journal May 1983
Repellers, semi-attractors, and long-lived chaotic transients journal August 1985
A paradigm for joined Hamiltonian and dissipative systems journal January 1986
A procedure for finding numerical trajectories on chaotic saddles journal June 1989
Area preserving nontwist maps: periodic orbits and transition to chaos journal March 1996
Strange saddles and the dimensions of their invariant manifolds journal February 1988
Integrable approximation to the overlap of resonances journal March 1992
The birth process of periodic orbits in non-twist maps journal November 1990
Units: Remarkable points in dynamical systems journal December 1995
Conformal Hamiltonian systems journal October 2001
Nontwist symplectic maps in tokamaks journal May 2012
A KAM theory for conformally symplectic systems: Efficient algorithms and their validation journal September 2013
Robust attractor of non-twist systems journal December 2015
Analysis of chaotic saddles in low-dimensional dynamical systems: the derivative nonlinear Schrödinger equation journal December 2004
Meanders and reconnection–collision sequences in the standard nontwist map journal June 2005
Routes to extreme events in dynamical systems: Dynamical and statistical characteristics journal June 2020
Chaotic transport by Rossby waves in shear flow journal April 1993
Chaotic transport in zonal flows in analogous geophysical and plasma systems journal May 2000
Magnetic field lines, Hamiltonian dynamics, and nontwist systems journal June 2000
Curry–Yorke route to shearless attractors and coexistence of attractors in dissipative nontwist systems
  • Mugnaine, Michele; Batista, Antonio M.; Caldas, Iberê L.
  • Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 31, Issue 2 https://doi.org/10.1063/5.0035303
journal February 2021
Conformal symplectic and relativistic optimization journal December 2020
Thoughts on brackets and dissipation: Old and new journal May 2009
Labyrinthic standard non-twist map journal December 2010
Destruction and resurgence of the quasiperiodic shearless attractor journal July 2021
Driving trajectories in chaotic scattering journal January 2002
Transport barriers with shearless attractors journal March 2019
Routes to chaotic scattering journal August 1989
Geometric Properties of the Chaotic Saddle Responsible for Supertransients in Spatiotemporal Chaotic Systems journal June 1995
Critical Exponent for Gap Filling at Crisis journal October 1996
Fractal structures in nonlinear dynamics journal March 2009
Tokamak magnetic field lines described by simple maps: Dedicated to Professor Celso Grebogi on the occasion of his 60th birthday journal December 2008
Nontwist area Preserving maps with Reversing Symmetry Group journal February 2001
On the role of Chaotic Saddles in Generating Chaotic Dynamics in Nonlinear Driven Oscillators journal April 2005
Diffusive Transport Through a Nontwist Barrier in Tokamaks journal May 2007
Roles of Chaotic Saddle and Basin of Attraction in Bifurcation and Crisis Analysis journal March 2011
The Chaotic Saddle in the Lozi Map, Autonomous and Nonautonomous Versions journal December 2015
Indicators of Reconnection Processes and Transition to Global Chaos in Nontwist Maps journal August 1998
Non-twist field line mappings for tokamaks with reversed magnetic shear journal December 2004
Twist and non-twist regimes of the oblate planet problem journal September 2017

Figures / Tables (18)

FIG. 1(p. 6)figure FIG. 1
FIG. 2(p. 10)figure FIG. 2
FIG. 3(p. 10)figure FIG. 3
FIG. 4(p. 11)figure FIG. 4
FIG. 5(p. 12)figure FIG. 5
FIG. 6(p. 13)figure FIG. 6
FIG. 7(p. 14)figure FIG. 7
FIG. 8(p. 15)figure FIG. 8
FIG. 10(p. 17)figure FIG. 10
FIG. 9(p. 17)figure FIG. 9
FIG. 11(p. 18)figure FIG. 11
FIG. 12(p. 19)figure FIG. 12
FIG. 13(p. 20)figure FIG. 13
FIG. 14(p. 21)figure FIG. 14
FIG. 15(p. 22)figure FIG. 15
FIG. 6(p. 22)figure FIG. 6
FIG. 17(p. 23)figure FIG. 17
FIG. 18(p. 24)figure FIG. 18

Similar Records

Global bifurcations in fractional-order chaotic systems with an extended generalized cell mapping method
Journal Article · Mon Aug 15 00:00:00 EDT 2016 · Chaos (Woodbury, N. Y.) · OSTI ID:22596614
Double crises in two-parameter dynamical systems
Journal Article · Mon Sep 25 00:00:00 EDT 1995 · Physical Review Letters · OSTI ID:239440
Direct observation of crises of the chaotic attractor in a nonlinear oscillator
Journal Article · Fri Dec 31 23:00:00 EST 1982 · Phys. Rev. A; (United States) · OSTI ID:6205167

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Physics