The New Theory of Nonlinear Differential and Difference Equations Based on Bifurcation Groups and Its Applications

Abstracts of 16th International Conference on Difference Equations and Applications 2010
Mihails Zakrževskis

A new approach for the global bifurcation analysis for nonlinear difference equations, based on the ideas of Poincar´e, Birkhoff and Andronov, is proposed. The main idea of the approach is a concept of complete bifurcation groups and periodic branch continuation along stable and unstable solutions, named by the author as a method of complete bifurcation groups (MCBG). The article is widely illustrated using difference nonlinear models with one-degree-of-freedom. Rare attractors in difference nonlinear models, can be found using the same approaches as for nonlinear ODE.

Atslēgas vārdi
Global bifurcation analysis, difference equations, method of complete bifurcation groups, rare attractors

Zakrževskis, M. The New Theory of Nonlinear Differential and Difference Equations Based on Bifurcation Groups and Its Applications. No: Abstracts of 16th International Conference on Difference Equations and Applications, Latvija, Rīga, 19.-23. jūlijs, 2010. Rīga: Latvijas Matemātikas biedrība, 2010, 60.-60.lpp. ISBN 978-9984-45-213-5.

Publikācijas valoda
English (en)