IRATE
发表于 2025-3-27 00:27:34
Introduction to the theory of stability, ideas pose difficult questions. In defining stability, this concept turns out to have many aspects. Also there is of course the problem that in investigating the stability of a special solution, one has to characterise the behaviour of a set of solutions. One solution is often difficult enough.
LUCY
发表于 2025-3-27 01:18:17
Bifurcation theory,-plane is a centre point. If the parameter is positive with 0 < μ < 1, the origin is an unstable focus and there exists an asymptotically stable periodic solution, corresponding with a limit cycle around the origin. Another important illustration of the part played by parameters is the forced Duffing-equation in section 10.3 and example 11.8.
Incisor
发表于 2025-3-27 09:02:30
Chaos,ems. We shall restrict ourselves to a discussion of two examples from the various domains where these phenomena have been found: autonomous differential equations with dimension . ≥ 3, second-order forced differential equations like the forced van der Pol- or the forced Duffing equation and mappings of ℝ into ℝ, ℝ. into ℝ. etc.
palpitate
发表于 2025-3-27 09:59:46
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细微的差异
发表于 2025-3-27 14:43:01
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Cerumen
发表于 2025-3-27 18:19:41
0172-5939 es and the research literature. The basic concepts necessary to study differential equations - critical points and equilibrium, periodic solutions, invariant sets and invariant manifolds - are discussed. Stability theory is developed starting with linearisation methods going back to Lyapunov and Poi
Flat-Feet
发表于 2025-3-28 01:21:40
Introduction, the form(1.1) $${dot x}= f(t,x)$$using Newton’s fluxie notation ẋ = .. The variable . is a scalar, . ∈ ℝ, often identified with time. The vector function . : . → ℝ. is continuous in . and .; . is an open subset of ℝ., so . ∈ ℝ..
咆哮
发表于 2025-3-28 05:32:56
Autonomous equations,f the form (2.1) is called autonomous. A scalar equation of order . is often written as(2.2) $$x^{(n)}+ F(x^{(n-1)},“ots ,x)=0$$in which . = . ./., . = 0,1, …, ., . = .In characterising the solutions of autonomous equations we shall use three special sets of solutions: . or . and ..
Buttress
发表于 2025-3-28 08:02:58
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欲望小妹
发表于 2025-3-28 10:52:11
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