Many problems in the natural and engineering sciences can be modeled as evolution processes. Mathematically this leads to either discrete or continuous dynamical systems, i.e. to either difference or differential equations. Usually such dynamical systems are nonlinear or even discontinuous and depend on parameters. Consequently the study of qualitative behaviour of their solutions is very difficult. Rather effective method for handling dynamical systems is the bifurcation theory, when the original problem is a perturbation of a solvable problem, and we are interested in qualitative changes of properties of solutions for small parameter variations. Nowadays the bifurcation and perturbation theories are well developed and methods applied by these theories are rather broad including functional-analytical tools and numerical simulations as well [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13].


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© Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Michal Fečkan
    • 1
  1. 1.Department of Mathematical Analysis and Numerical Mathematics Faculty of Mathematics, Physics and InformaticsComenius University Mlynská dolinaBratislavaSlovakia

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