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- W83146239 abstract "A dynamical system is a mathematical object to describe the development of a physical, biological or another system from real life depending on time. It is defined by a phase space M, and by a one-parameter family of mappings ϕt: M → M, where t is the parameter (the time). In the following, the phase space is often ℝn, a subset of it, or a metric space. The time parameter t is from ℝ (time continuous system) or from ℤ or from ℤ+ (time discrete system). Furthermore, it is required for arbitrary x ∈ M that a) ϕ0(x) = x and b) ϕt(ϕs(x))=ϕt+s(x) for all t, s. The mapping ϕ1 is denoted briefly by ϕ. In the following, the time set is denoted by Г, hence, Г = ℝ,Г = ℝ+,Г = ℤ or Г=ℤ+. If Г = ℝ, then the dynamical system is also called a flow; if Г = ℝ or Г = ℝ+, then the dynamical system is discrete. In case Г = ℝ and Г = ℤ, the properties a) and b) are satisfied for every t ∈ Г, so the inverse mapping (ϕt)−1 = ϕ−t also exists, and these systems are called invertible dynamical systems.KeywordsPeriodic OrbitHopf BifurcationRotation NumberSupercritical Hopf BifurcationHausdor DimensionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
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- W83146239 date "2007-08-14" @default.
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- W83146239 title "Dynamical Systems and Chaos" @default.
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- W83146239 doi "https://doi.org/10.1007/978-3-540-72122-2_17" @default.
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