Numerical methods for bifurcations of dynamical equilibria

By:

Govaerts, Willy J. F

Publication details: Philadelphia: Society for Industrial and Applied Mathematics (SIAM), 2000.Description: xxii, 362p.: pbk.: 26 cmISBN:

9780898714425

Subject(s):

DDC classification:

515.35221 GOC

Summary: Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra. Several features make this book unique. The first is the systematic use of bordered matrix methods in the numerical computation and continuation of various bifurcations. The second is a detailed treatment of bialternate matrix products and their Jordan structure. Govaerts discusses their use in the numerical methods for Hopf and related bifurcations. A third feature is a unified treatment of singularity theory, with and without a distinguished bifurcation parameter, from a numerical point of view. Finally, numerical methods for symmetry-breaking bifurcations are discussed in detail, up to the fundamental cases covered by the equivariant branching lemma. https://epubs.siam.org/doi/10.1137/1.9780898719543

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Item type	Current library	Collection	Call number	Copy number	Status	Barcode
Books	IIT Gandhinagar	General	515.35221 GOC (Browse shelf(Opens below))	1	Available	036324

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Previous	515.352 TRE Exploring ODEs	515.352 WAS Asymptotic expansions for ordinary differential equations	515.352 WIT Methods of mathematical modelling: continuous systems and differential equations	515.35221 GOC Numerical methods for bifurcations of dynamical equilibria	515.353 CAR Nonsmooth variational problems and their inequalities : comparison principles and applications	515.353 AMB Optimal transportation and applications: lectures given at the C.I.M.E. summer school held in Martina Franca, Italy, September 2–8, 2001	515.353 BAR Numerical methods for nonlinear partial differential equations	Next

Includes Bibliography and Index.

Dynamical systems arise in all fields of applied mathematics. The author focuses on the description of numerical methods for the detection, computation, and continuation of equilibria and bifurcation points of equilibria of dynamical systems. This subfield has the particular attraction of having links with the geometric theory of differential equations, numerical analysis, and linear algebra.

Several features make this book unique. The first is the systematic use of bordered matrix methods in the numerical computation and continuation of various bifurcations. The second is a detailed treatment of bialternate matrix products and their Jordan structure. Govaerts discusses their use in the numerical methods for Hopf and related bifurcations. A third feature is a unified treatment of singularity theory, with and without a distinguished bifurcation parameter, from a numerical point of view. Finally, numerical methods for symmetry-breaking bifurcations are discussed in detail, up to the fundamental cases covered by the equivariant branching lemma.

https://epubs.siam.org/doi/10.1137/1.9780898719543

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