zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The use of the Euler method in identification of multiple bifurcations and chaotic behavior in numerical approximation of delay-differential equations. (English) Zbl 1054.65126
Summary: A discrete model is proposed to delve into the rich dynamics of nonlinear delayed systems under Euler discretization, such as multiple bifurcations, stable limit cycles (periodic or quasiperiodic solutions), and chaotic behavior. A method of using a finite-dimensional discrete dynamical system to approximate an infinite-dimensional dynamical system is developed here. We find that the effect of breaking the symmetry of the system is to create a wide complex operating conditions which would not otherwise be seen. These include complex periodic oscillations, quasiperiodicity and chaos. A route from complex periodic/quasiperiodic oscillations to chaos and then to quasiperiodic oscillations can be observed. The delay model also gives a family of examples for chaotic behavior usable to demonstrate analyzing, controlling and anti-controlling schemes.
65P30Bifurcation problems (numerical analysis)
37M20Computational methods for bifurcation problems
37D45Strange attractors, chaotic dynamics
37G15Bifurcations of limit cycles and periodic orbits
34K28Numerical approximation of solutions of functional-differential equations
37K50Bifurcation problems (infinite-dimensional systems)