Unstable dimension variability structure in the parameter space of coupled Hénon maps

Vagner Dos Santos; José D. Szezech; Murilo S. Baptista; Antonio M. Batista; Iberê L. Caldas

doi:10.1016/j.amc.2016.04.007

Unstable dimension variability structure in the parameter space of coupled Hénon maps

Vagner Dos Santos, José D. Szezech^*, Murilo S. Baptista, Antonio M. Batista, Iberê L. Caldas

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

Coupled maps have been investigated to model the applications of periodic and chaotic dynamics of spatially extended systems. We have studied the parameter space of coupled Hénon maps and showed that attractors possessing unstable dimension variability (UDV) appear for parameters neighbouring the so called shrimp domains, representing parameters leading to stable periodic behaviour. Therefore, the UDV should be very likely to be found in the same large class of natural and man-made systems that present shrimp domains.

Original language	English
Pages (from-to)	23-28
Number of pages	6
Journal	Applied Mathematics and Computation
Volume	286
Early online date	22 Apr 2016
DOIs	https://doi.org/10.1016/j.amc.2016.04.007
Publication status	Published - 5 Aug 2016

Bibliographical note

Acknowledgements
This study was possible by partial financial support from the following agencies: Fundação Araucária, EPSRC-EP/I032606/1, CNPq, CAPES, and FAPESP 2011/19296-1.

Keywords

Hénon map
Lyapunov exponents
Parameter-space
Shrimp
UDV

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title = "Unstable dimension variability structure in the parameter space of coupled H{\'e}non maps",

abstract = "Coupled maps have been investigated to model the applications of periodic and chaotic dynamics of spatially extended systems. We have studied the parameter space of coupled H{\'e}non maps and showed that attractors possessing unstable dimension variability (UDV) appear for parameters neighbouring the so called shrimp domains, representing parameters leading to stable periodic behaviour. Therefore, the UDV should be very likely to be found in the same large class of natural and man-made systems that present shrimp domains.",

keywords = "H{\'e}non map, Lyapunov exponents, Parameter-space, Shrimp, UDV",

author = "{Dos Santos}, Vagner and Szezech, {Jos{\'e} D.} and Baptista, {Murilo S.} and Batista, {Antonio M.} and Caldas, {Iber{\^e} L.}",

note = "Acknowledgements This study was possible by partial financial support from the following agencies: Funda{\c c}{\~a}o Arauc{\'a}ria, EPSRC-EP/I032606/1, CNPq, CAPES, and FAPESP 2011/19296-1.",

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AU - Szezech, José D.

AU - Baptista, Murilo S.

AU - Batista, Antonio M.

AU - Caldas, Iberê L.

N1 - Acknowledgements This study was possible by partial financial support from the following agencies: Fundação Araucária, EPSRC-EP/I032606/1, CNPq, CAPES, and FAPESP 2011/19296-1.

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N2 - Coupled maps have been investigated to model the applications of periodic and chaotic dynamics of spatially extended systems. We have studied the parameter space of coupled Hénon maps and showed that attractors possessing unstable dimension variability (UDV) appear for parameters neighbouring the so called shrimp domains, representing parameters leading to stable periodic behaviour. Therefore, the UDV should be very likely to be found in the same large class of natural and man-made systems that present shrimp domains.

AB - Coupled maps have been investigated to model the applications of periodic and chaotic dynamics of spatially extended systems. We have studied the parameter space of coupled Hénon maps and showed that attractors possessing unstable dimension variability (UDV) appear for parameters neighbouring the so called shrimp domains, representing parameters leading to stable periodic behaviour. Therefore, the UDV should be very likely to be found in the same large class of natural and man-made systems that present shrimp domains.

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KW - Lyapunov exponents

KW - Parameter-space

KW - Shrimp

KW - UDV

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JO - Applied Mathematics and Computation

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Unstable dimension variability structure in the parameter space of coupled Hénon maps

Abstract

Bibliographical note

Keywords

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