Exploring the qualitative behavior of uncertain dynamical systems: A computational approach

Authors: Edwin Kreuzer, Andreas Gaull

Source: Nonlinear Dynamics. 63:285-310

Subject Terms: Computational methods in stochastic control, 16. Peace & justice, ergodic decomposition, 01 natural sciences, transition operator, colored noise, cell mapping, 0103 physical sciences, nonlinear dynamical systems, 0101 mathematics, uncertainty, Generation, random and stochastic difference and differential equations, Computational methods for stochastic equations (aspects of stochastic analysis), Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: https://zbmath.org/5916603
https://doi.org/10.1007/s11071-010-9804-5
https://link.springer.com/10.1007%2Fs11071-010-9804-5
https://link.springer.com/article/10.1007%2Fs11071-010-9804-5

Symbolic mathematical computing of bifurcations in dynamical systems

Authors: J. A. Martínez, Fernando L. Pelayo, J. J. Miralles, Jose C. Valverde

Source: Journal of Computational Methods in Sciences and Engineering. 4:115-123

Subject Terms: Bifurcations of singular points in dynamical systems, computational mathematics, Normal forms for dynamical systems, Discrete-time control/observation systems, symbolic mathematical computing, Symbolic dynamics, computational engineering, 0101 mathematics, fixed points of maps, bifurcations, 01 natural sciences, Approximation methods and numerical treatment of dynamical systems, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: https://zbmath.org/2156354
https://content.iospress.com/articles/journal-of-computational-methods-in-sciences-and-engineering/jcm00014
https://dblp.uni-trier.de/db/journals/jcmse/jcmse4.html#ValverdePMC04
http://dblp.uni-trier.de/db/journals/jcmse/jcmse4.html#ValverdePMC04

Accurate computation of component centers in the degree-n bifurcation set: Accurate computation of component centers in the degree-\(n\) bifurcation set

Authors: Young Hee Geum, Young Ik Kim

Source: Computers & Mathematics with Applications. 48:163-175

Subject Terms: Component centers, Degree-n bifurcation set, 02 engineering and technology, 01 natural sciences, Dynamics of complex polynomials, rational maps, entire and meromorphic functions, Fatou and Julia sets, bifurcation set, Computational Mathematics, Newton's method, Computational Theory and Mathematics, Modelling and Simulation, Numerical bifurcation problems, 0103 physical sciences, Mandelbrot set, 0202 electrical engineering, electronic engineering, information engineering, Bifurcation, Holomorphic families of dynamical systems, the Mandelbrot set, bifurcations, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: https://zbmath.org/2142454
https://doi.org/10.1016/j.camwa.2003.08.006
https://core.ac.uk/display/82382210
https://www.sciencedirect.com/science/article/pii/S0898122104840070

Computing One-Dimensional Stable Manifolds and Stable Sets of Planar Maps without the Inverse: Computing one-dimensional stable manifolds and stable sets of planar maps without the inverse

Authors: James P. England, Bernd Krauskopf, Hinke M. Osinga

Source: SIAM Journal on Applied Dynamical Systems. 3:161-190

Subject Terms: planar map, piecewise-smooth map, discrete-time system, Invariant manifold theory for dynamical systems, Low-dimensional dynamical systems, 01 natural sciences, Numerical bifurcation problems, 0103 physical sciences, SDG 7 - Affordable and Clean Energy, Computational methods for bifurcation problems in dynamical systems, noninvertible map, stable set, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory, stable manifold

File Description: application/xml

Access URL: https://epubs.siam.org/doi/pdf/10.1137/030600131

A renormalization group fixed point associated with the breakup of golden invariant tori

Authors: Hans Koch

Source: Discrete & Continuous Dynamical Systems - A. 11:881-909

Subject Terms: Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, Hamiltonian flow, Nearly integrable Hamiltonian systems, KAM theory, Universality and renormalization of dynamical systems, 0103 physical sciences, renormalization group, 0101 mathematics, golden ratio, 01 natural sciences, Renormalization group methods in equilibrium statistical mechanics, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: https://www.aimsciences.org/article/doi/10.3934/dcds.2004.11.881

The holomorphic flow of the Riemann zeta function

Authors: Kevin A. Broughan, A. Ross Barnett

Source: Mathematics of Computation. 73:987-1004

Subject Terms: plotting techniques, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), \(\zeta (s)\) and \(L(s, \chi)\), Analytic computations, 0103 physical sciences, separatrix, Special classes of entire functions of one complex variable and growth estimates, phase portrait, Dynamical aspects of holomorphic foliations and vector fields, 01 natural sciences, dynamical system, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory, Riemann zeta-function

File Description: application/xml

Access URL: https://www.ams.org/mcom/2004-73-246/S0025-5718-03-01529-1/S0025-5718-03-01529-1.pdf
https://www.ams.org/mcom/2004-73-246/S0025-5718-03-01529-1/home.html
https://researchcommons.waikato.ac.nz/bitstream/handle/10289/1263/AMS%20Broughan%20Riemann%20zeta.pdf;sequence=1
http://ui.adsabs.harvard.edu/abs/2004MaCom..73..987B/abstract
https://doi.org/10.1090/S0025-5718-03-01529-1
https://researchcommons.waikato.ac.nz/handle/10289/1263
https://www.ams.org/mcom/2004-73-246/S0025-5718-03-01529-1/S0025-5718-03-01529-1.pdf

The H non–Heiles Hamiltonian near the critical energy level—some rigorous results: The Hénon-Heiles Hamiltonian near the critical energy level. Some rigorous results.

Authors: ARIOLI, GIANNI, P. Zgliczynski

Source: Nonlinearity. 16:1833-1852

Subject Terms: chaotic dynamics, homoclinic solutions, Symbolic dynamics, Symmetries, equivariant dynamical systems, Periodic, homoclinic and heteroclinic orbits, variational methods, degree-theoretic methods, 01 natural sciences, Strange attractors, chaotic dynamics of systems with hyperbolic behavior, numerical simulations, symmetric hyperbolic periodic solutions, heteroclinic solutions, Periodic orbits of vector fields and flows, Homoclinic and heteroclinic orbits for dynamical systems, 0101 mathematics, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory, elliptic periodic solutions

File Description: application/xml

Access URL: https://ui.adsabs.harvard.edu/abs/2003Nonli..16.1833A/abstract
https://re.public.polimi.it/handle/11311/557090
http://iopscience.iop.org/article/10.1088/0951-7715/16/5/316
https://ruj.uj.edu.pl/xmlui/handle/item/80807
http://www.iop.org/EJ/abstract/0951-7715/16/5/316/
https://hdl.handle.net/11311/557090

MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs

Authors: Willy Govaerts, Yu. A. Kuznetsov, Annick Dhooge

Source: ACM Transactions on Mathematical Software. 29:141-164

Subject Terms: Landbouwwetenschappen, Wiskunde: algemeen, Numerical bifurcation problems, Bifurcations of limit cycles and periodic orbits in dynamical systems, Wiskunde en computerwetenschappen, Packaged methods for numerical algorithms, Computational methods for bifurcation problems in dynamical systems, Mathematics, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: https://zbmath.org/2187847
https://doi.org/10.1145/779359.779362
https://research-portal.uu.nl/en/publications/a4ce7393-b48b-409b-a101-1af4faeeed83
https://biblio.ugent.be/publication/209719
https://dl.acm.org/doi/10.1145/779359.779362
http://portal.acm.org/citation.cfm?doid=779359.779362
http://www.sigsam.org/issac/2003/Software/Dhooge.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=2646239
https://dl.acm.org/citation.cfm?id=779362

COMPUTING INVARIANT SETS: Computing invariant sets.

Authors: Duncan Sands, Robin de Vilder, Ale Jan Homburg

Source: International Journal of Bifurcation and Chaos. 13:497-504

Subject Terms: invariant set, Stable manifold, numerical algorithm, Invariant manifold theory for dynamical systems, 0101 mathematics, 01 natural sciences, Approximation methods and numerical treatment of dynamical systems, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: https://dare.uva.nl/personal/pure/en/publications/computing-invariant-sets(ca35d372-41e0-464c-80b6-de3fb60e8ef8).html
https://hdl.handle.net/11245/1.212919
https://doi.org/10.1142/S0218127403006674
https://www.narcis.nl/publication/RecordID/oai%3Adare.uva.nl%3Apublications%2Fca35d372-41e0-464c-80b6-de3fb60e8ef8
https://dblp.uni-trier.de/db/journals/ijbc/ijbc13.html#HomburgVS03
https://www.worldscientific.com/doi/10.1142/S0218127403006674
https://ui.adsabs.harvard.edu/abs/2003IJBC...13..497H/abstract

Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles: Detecting and locating near-optimal almost-invariant sets and cycles

Authors: Gary Froyland, Michael Dellnitz

Source: SIAM Journal on Scientific Computing. 24:1839-1863

Subject Terms: Connectivity, almost-invariant set, graph partitioning, maximal cut, Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.), 01 natural sciences, almost cycle, minimal cut, macrostructure, Fiedler vector, 0103 physical sciences, 0101 mathematics, Laplacian matrix, Smooth ergodic theory, invariant measures for smooth dynamical systems, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

AN EFFICIENT METHOD FOR COMPUTING THE SIMPLEST NORMAL FORMS OF VECTOR FIELDS: An efficient method for computing the simplest normal forms of vector fields.

Authors: Yuan Yuan, Pei Yu

Source: International Journal of Bifurcation and Chaos. 13:19-46

Subject Terms: recursive algorithm, Normal forms for dynamical systems, MAPLE, SNF, B-T singularity, 01 natural sciences, efficient computation, CNF, 0103 physical sciences, Software, source code, etc. for problems pertaining to ordinary differential equations, Hopf bifurcation, 0101 mathematics, computer algebra, Transformation and reduction of ordinary differential equations and systems, normal forms, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: http://ui.adsabs.harvard.edu/abs/2003IJBC...13...19Y/abstract
https://www.worldscientific.com/doi/abs/10.1142/S0218127403006418
https://ui.adsabs.harvard.edu/abs/2003IJBC...13...19Y/abstract
https://dblp.uni-trier.de/db/journals/ijbc/ijbc13.html#YuY03

Analysis on Double Hopf Bifurcation Using Computer Algebra with the Aid of Multiple Scales: Analysis on double Hopf bifurcation using computer algebra with the aid of multiple scales

Authors: Pei Yu

Source: Nonlinear Dynamics. 27:19-53

Subject Terms: critical point, stability, Stability theory for smooth dynamical systems, Symbolic computation and algebraic computation, 01 natural sciences, normal form, Numerical bifurcation problems, bifurcation, 0103 physical sciences, nonlinear dynamical systems, Computational methods for bifurcation problems in dynamical systems, computer algebra, Numerical nonlinear stabilities in dynamical systems, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: https://zbmath.org/1747902
https://doi.org/10.1023/a:1017993026651
https://link.springer.com/article/10.1023/A%3A1017993026651
https://link.springer.com/10.1023/A:1017993026651

analysis on double hopf bifurcation using computer algebra with the aid of multiple scales: Analysis on double Hopf bifurcation using computer algebra with the aid of multiple scales

Authors: Pei Yu

Source: Nonlinear Dynamics. 27(1):19-53

Subject Terms: normal form, Numerical bifurcation problems, bifurcation, critical point, nonlinear dynamical systems, Computational methods for bifurcation problems in dynamical systems, stability, Stability theory for smooth dynamical systems, Symbolic computation and algebraic computation, computer algebra, Numerical nonlinear stabilities in dynamical systems, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: https://zbmath.org/1747902
https://doi.org/10.1023/a:1017993026651
https://link.springer.com/article/10.1023/A%3A1017993026651
https://link.springer.com/10.1023/A:1017993026651

Global fit of ab initio potential energy surfaces: II.2. Tetratomic systems A2B2 and ABC2: Global fit of ab initio potential energy surfaces. II.2: Tetratomic systems \(A_2B_2\) and \(ABC_2\)

Authors: Alfredo Aguado, Miguel Paniagua, César Tablero

Source: Computer Physics Communications. 140:412-417

Subject Terms: Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics), Software, source code, etc. for problems pertaining to quantum theory, 0103 physical sciences, 02 engineering and technology, Molecular physics, Numerical methods for Hamiltonian systems including symplectic integrators, 0210 nano-technology, Computational methods for problems pertaining to quantum theory, 01 natural sciences, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: https://www.sciencedirect.com/science/article/abs/pii/S0010465501002892
https://ui.adsabs.harvard.edu/abs/2001CoPhC.140..412T/abstract

Visualization and analysis of invariant sets of dynamical systems: Visualization and analysis of invariant sets of dynamical systems.

Authors: A.D. Morozov, T.N. Dragunov

Source: Nonlinear Analysis. 47:5285-5296

Subject Terms: 0101 mathematics, 01 natural sciences, Approximation methods and numerical treatment of dynamical systems, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: https://zbmath.org/2095347
https://doi.org/10.1016/s0362-546x(01)00635-6
https://www.sciencedirect.com/science/article/pii/S0362546X01006356#!

Integrable evolution equations in time-dependent domains

Authors: Beatrice Pelloni, Athanasios S. Fokas

Source: Inverse Problems. 17:919-935

Subject Terms: Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems, compatibility condition, NLS equations (nonlinear Schrödinger equations), dispersive linear evolution equation, 0103 physical sciences, defocusing nonlinear Schrödinger equation, Lax pair formulation, 0101 mathematics, implementation, 01 natural sciences, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: https://zbmath.org/1657914
https://doi.org/10.1088/0266-5611/17/4/323
https://centaur.reading.ac.uk/7583/
http://ui.adsabs.harvard.edu/abs/2001InvPr..17..919F/abstract
https://core.ac.uk/display/345701
https://researchportal.hw.ac.uk/en/publications/integrable-evolution-equations-in-time-dependent-domains
http://iopscience.iop.org/article/10.1088/0266-5611/17/4/323/pdf

On Computer-assisted Classification of Coupled Integrable Equations: On computer-assisted classification of coupled integrable equations

Authors: Marc Moreno Maza, Mikhail V. Foursov

Source: Journal of Symbolic Computation. 33:647-660

Subject Terms: Computational Mathematics, Algebra and Number Theory, KdV equations (Korteweg-de Vries equations), coupled integrable equations, evolution equations, triangularization algorithm, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Gröbner bases, other bases for ideals and modules (e.g., Janet and border bases), 0101 mathematics, Symbolic computation and algebraic computation, 01 natural sciences, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: https://dblp.uni-trier.de/db/conf/issac/issac2001.html#FoursovM01
https://www.csd.uwo.ca/~moreno/Publications/Foursov-MorenoMaza-2002-JSC.pdf
http://doi.org/10.1145/384101.384120
https://core.ac.uk/display/20907104
https://doi.org/10.1145/384101.384120
https://dl.acm.org/doi/10.1145/384101.384120
https://dialnet.unirioja.es/servlet/articulo?codigo=315255
https://dl.acm.org/doi/10.1006/jsco.2002.0527
https://core.ac.uk/display/24693411
https://dblp.uni-trier.de/db/journals/jsc/jsc33.html#FoursovM02
https://www.sciencedirect.com/science/article/pii/S0747717102905274
https://www.sciencedirect.com/science/article/abs/pii/S0747717102905274

The Applications of a Modified Normal Form Approach: The applications of a modified normal form approach.

Authors: Huseyin Koncay, Wei-yi Zhang, Min Ye

Source: Applied Mathematics and Mechanics. 22:802-807

Subject Terms: 0203 mechanical engineering, Local and nonlocal bifurcation theory for dynamical systems, 0103 physical sciences, nonlinear dynamical system, symbolic calculations, 02 engineering and technology, 0101 mathematics, 01 natural sciences, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory, modified normal form approach, 0201 civil engineering

File Description: application/xml

Access URL: https://zbmath.org/1661461
https://doi.org/10.1023/a:1016309403447
https://link.springer.com/article/10.1007/BF02438224
https://www.amm.shu.edu.cn/CN/abstract/abstract12357.shtml

Computation of the coefficients associated with the normal form of a resonant five-dimensional system: Computation of the coefficients associated with the normal form of a resonant five-dimensional system.

Authors: Koncay Huseyin, W. Zhang

Source: Mathematical and Computer Modelling. 30:213-228

Subject Terms: Normal forms for dynamical systems, Modelling and Simulation, Software, source code, etc. for problems pertaining to ordinary differential equations, 02 engineering and technology, 0101 mathematics, 0210 nano-technology, 01 natural sciences, Transformation and reduction of ordinary differential equations and systems, normal forms, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory, Computer Science Applications

File Description: application/xml

Access URL: https://zbmath.org/1737710
https://doi.org/10.1016/s0895-7177(99)00209-5
http://www.sciencedirect.com/science/article/pii/S0895717799002095
https://www.sciencedirect.com/science/article/pii/S0895717799002095

SIMILARITY REDUCTIONS FOR A GENERALIZED VARIABLE-COEFFICIENT KADOMTSEV–PETVIASHVILI EQUATION WITH SYMBOLIC COMPUTATION: Similarity reductions for a generalized variable-coefficient Kadomtsev-Petviashvili equation with symbolic computation

Authors: Bo Tian

Source: International Journal of Modern Physics C. 10:1089-1097

Subject Terms: KdV equations (Korteweg-de Vries equations), water waves, generalized Kadomtsev-Petviashvili equation, 0103 physical sciences, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions, similarity reductions, Painlevé conjecture, 01 natural sciences, symbolic computation, Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory

File Description: application/xml

Access URL: https://zbmath.org/1470629
https://doi.org/10.1142/s0129183199000899
https://ui.adsabs.harvard.edu/abs/1999IJMPC..10.1089T/abstract