The routes to chaos play an important role in predictions about the transitions from regular to irregular behavior in nonlinear dynamical systems, such as electrical oscillators, chemical reactions, biomedical rhythms, and nonlinear wave coupling. Of special interest are dissipative systems obtained by adding a dissipation term in a given Hamiltonian system. If the latter satisfies the so-called twist property, the corresponding dissipative version can be called a “dissipative twist system.” Transitions to chaos in these systems are well established; for instance, the Curry–Yorke route describes the transition from a quasiperiodic attractor on torus to chaos passing by a chaotic banded attractor. In this paper, we study the transitions from an attractor on torus to chaotic motion in dissipative nontwist systems. We choose the dissipative standard nontwist map, which is a non-conservative version of the standard nontwist map. In our simulations, we observe the same transition to chaos that happens in twist systems, known as a soft one, where the quasiperiodic attractor becomes wrinkled and then chaotic through the Curry–Yorke route. By the Lyapunov exponent, we study the nature of the orbits for a different set of parameters, and we observe that quasiperiodic motion and periodic and chaotic behavior are possible in the system. We observe that they can coexist in the phase space, implying in multistability. The different coexistence scenarios were studied by the basin entropy and by the boundary basin entropy.
Skip Nav Destination
Curry–Yorke route to shearless attractors and coexistence of attractors in dissipative nontwist systems
,
,
,
,
,
Article navigation
February 2021
Research Article|
February 16 2021
Curry–Yorke route to shearless attractors and coexistence of attractors in dissipative nontwist systems
Available to Purchase
Special Collection:
Recent Advances in Modeling Complex Systems: Theory and Applications
Michele Mugnaine
;
Michele Mugnaine
1
Department of Physics, Federal University of Paraná
, 80060-000 Curitiba, PR, Brazil
Search for other works by this author on:
Antonio M. Batista;
Antonio M. Batista
2
Department of Mathematics and Statistics, State University of Ponta Grossa
, 84030-900 Ponta Grossa, PR, Brazil
3
Graduate in Science Program—Physics, State University of Ponta Grossa
, 84030-900 Ponta Grossa, PR, Brazil
4
Institute of Physics, University of São Paulo
, 05508-900 São Paulo, SP, Brazil
Search for other works by this author on:
Iberê L. Caldas
;
Iberê L. Caldas
4
Institute of Physics, University of São Paulo
, 05508-900 São Paulo, SP, Brazil
Search for other works by this author on:
José D. Szezech, Jr.
;
José D. Szezech, Jr.
a)
2
Department of Mathematics and Statistics, State University of Ponta Grossa
, 84030-900 Ponta Grossa, PR, Brazil
3
Graduate in Science Program—Physics, State University of Ponta Grossa
, 84030-900 Ponta Grossa, PR, Brazil
a)Author to whom correspondence should be addressed: [email protected]
Search for other works by this author on:
Ricardo Egydio de Carvalho;
Ricardo Egydio de Carvalho
5
Department of Statistics, Applied Mathematics and Computer Science, Institute of Geosciences and Exact Sciences—IGCE, São Paulo State University (UNESP)
, 13506-900 Rio Claro, SP, Brazil
Search for other works by this author on:
Ricardo L. Viana
Ricardo L. Viana
1
Department of Physics, Federal University of Paraná
, 80060-000 Curitiba, PR, Brazil
Search for other works by this author on:
Michele Mugnaine
1
Antonio M. Batista
2,3,4
Iberê L. Caldas
4
José D. Szezech, Jr.
2,3,a)
Ricardo Egydio de Carvalho
5
Ricardo L. Viana
1
1
Department of Physics, Federal University of Paraná
, 80060-000 Curitiba, PR, Brazil
2
Department of Mathematics and Statistics, State University of Ponta Grossa
, 84030-900 Ponta Grossa, PR, Brazil
3
Graduate in Science Program—Physics, State University of Ponta Grossa
, 84030-900 Ponta Grossa, PR, Brazil
4
Institute of Physics, University of São Paulo
, 05508-900 São Paulo, SP, Brazil
5
Department of Statistics, Applied Mathematics and Computer Science, Institute of Geosciences and Exact Sciences—IGCE, São Paulo State University (UNESP)
, 13506-900 Rio Claro, SP, Brazil
a)Author to whom correspondence should be addressed: [email protected]
Note: This paper is part of the Focus Issue, Recent Advances in Modeling Complex Systems: Theory and Applications.
Chaos 31, 023125 (2021)
Article history
Received:
October 27 2020
Accepted:
January 22 2021
Citation
Michele Mugnaine, Antonio M. Batista, Iberê L. Caldas, José D. Szezech, Ricardo Egydio de Carvalho, Ricardo L. Viana; Curry–Yorke route to shearless attractors and coexistence of attractors in dissipative nontwist systems. Chaos 1 February 2021; 31 (2): 023125. https://doi.org/10.1063/5.0035303
Download citation file:
Pay-Per-View Access
$40.00
Sign In
You could not be signed in. Please check your credentials and make sure you have an active account and try again.
Citing articles via
Reservoir computing with the minimum description length principle
Antony Mizzi, Michael Small, et al.
Recent achievements in nonlinear dynamics, synchronization, and networks
Dibakar Ghosh, Norbert Marwan, et al.
Data-driven nonlinear model reduction to spectral submanifolds via oblique projection
Leonardo Bettini, Bálint Kaszás, et al.
Related Content
Shearless and periodic attractors in the dissipative Labyrinthic map
Chaos (December 2024)
Breakup of shearless meanders and “outer” tori in the standard nontwist map
Chaos (August 2006)
Ratchet current in nontwist Hamiltonian systems
Chaos (September 2020)
Secondary nontwist phenomena in area-preserving maps
Chaos (September 2012)
Secondary shearless bifurcations for two isochronous resonant perturbations
Chaos (April 2025)