Abstract
In the natural sciences, it turns out that the formulation of mathematical models leads to temporal evolution laws for state variables that depend on parameters. The values of these parameters are defined by system elements that do not change over time. When described mathematically, a wide class of physical problems lead to differential equations or maps which depend on one or several parameters. Fixing parameter values determines the type of solutions for given initial conditions, while variation of these values may result in both quantitative and qualitative changes in the nature of the solutions.
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Notes
- 1.
Higher powers of a must also be taken into consideration when investigating the nature of bifurcation in the particular (degenerate) case L 1 = 0.
- 2.
Smale’s horseshoe is described in detail in Chap. 10.
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Anishchenko, V.S., Vadivasova, T.E., Strelkova, G.I. (2014). Bifurcations of Dynamical Systems. In: Deterministic Nonlinear Systems. Springer Series in Synergetics. Springer, Cham. https://doi.org/10.1007/978-3-319-06871-8_3
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