Titlebook: Nonlinear Differential Equations and Dynamical Systems; Ferdinand Verhulst Textbook 19901st edition Springer-Verlag Berlin Heidelberg 1990

IRATE

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

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

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

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Cerumen

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

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

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

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