Calculation of homoclinic and heteroclinic orbits in 1D maps

被引:8
作者
Avrutin, Viktor [1 ,3 ]
Schenke, Bjoern [2 ]
Gardini, Laura [3 ]
机构
[1] Univ Stuttgart, IST, Stuttgart, Germany
[2] Univ Stuttgart, IPVS, Stuttgart, Germany
[3] Univ Urbino, DESP, I-61029 Urbino, Italy
关键词
Homoclinic orbits; Heteroclinic connections; Algorithms; Homoclinic and heteroclinic bifurcations; Piecewise smooth maps; Discontinuous maps; Chaotic attractors; SNAP-BACK REPELLERS; CHAOTIC ATTRACTORS; ROBUST CHAOS; SCENARIO; CRISIS;
D O I
10.1016/j.cnsns.2014.07.008
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Homoclinic orbits and heteroclinic connections are important in several contexts, in particular for a proof of the existence of chaos and for the description of bifurcations of chaotic attractors. In this work we discuss an algorithm for their numerical detection in smooth or piecewise smooth, continuous or discontinuous maps. The algorithm is based on the convergence of orbits in backward time and is therefore applicable to expanding fixed points and cycles. For simplicity, we present the algorithm using 1D maps. (C) 2014 The Authors. Published by Elsevier B.V.
引用
收藏
页码:1201 / 1214
页数:14
相关论文
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[21]   A novel family of 1-D robust chaotic maps [J].
Mandal, Dhrubajyoti .
APPLIED MATHEMATICS AND NONLINEAR SCIENCES, 2021, 6 (01) :507-514
[22]   An FCT finite element scheme for ideal MHD equations in 1D and 2D [J].
Basting, Melanie ;
Kuzmin, Dmitri .
JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 338 :585-605
[23]   Influence of 3D effects on 1D aerosol retrievalsin synthetic, partially clouded scenes [J].
Stap, F. A. ;
Hasekamp, O. P. ;
Emde, C. ;
Rockmann, T. .
JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, 2016, 170 :54-68
[24]   Rapid mixing of path integral Monte Carlo for 1D stoquastic Hamiltonians [J].
Crosson, Elizabeth ;
Harrow, Aram W. .
QUANTUM, 2021, 5
[25]   Coupling strategies for the numerical simulation of blood flow in deformable arteries by 3D and 1D models [J].
Nobile, F. .
MATHEMATICAL AND COMPUTER MODELLING, 2009, 49 (11-12) :2152-2160
[26]   From 1D Endomorphism to Multidimensional Hénon Map: Persistence of Bifurcation Structure [J].
Belykh, V. N. ;
Barabash, N. V. ;
Grechko, D. A. .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2024, 34 (02)
[27]   Statistical Characterization of Acoustic Signals Using 1D Wavelet Transforms with Applications in Acoustical Oceanography [J].
Taroudakis, Michael I. .
JOURNAL OF THEORETICAL AND COMPUTATIONAL ACOUSTICS, 2018, 26 (04)
[28]   Quasi-interpolating bivariate dual v2-subdivision using 1D stencils [J].
Fang, Lincong ;
Han, Bin ;
Shen, Yi .
COMPUTER AIDED GEOMETRIC DESIGN, 2022, 98
[29]   A Limited-Memory Framework for Conditional Point Sampling for Radiation Transport in 1D Stochastic Media [J].
Vu, Emily H. ;
Olson, Aaron J. .
NUCLEAR SCIENCE AND ENGINEERING, 2023, 197 (02) :212-232
[30]   Helio1D modeling of temporal variation of solar wind: Interfacing between MULTI-VP and 1D MHD for future operational forecasting at L1 [J].
Kieokaew, R. ;
Pinto, R. F. ;
Samara, E. ;
Tao, C. ;
Indurain, M. ;
Lavraud, B. ;
Brunet, A. ;
Genot, V. ;
Rouillard, A. ;
Andre, N. ;
Bourdarie, S. ;
Katsavrias, C. ;
Darrouzet, F. ;
Grison, B. ;
Daglis, I. .
JOURNAL OF SPACE WEATHER AND SPACE CLIMATE, 2024, 14