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Erschienen in:
1990 | OriginalPaper | Buchkapitel
Autonomous equations
verfasst von : Ferdinand Verhulst
Erschienen in: Nonlinear Differential Equations and Dynamical Systems
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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In this chapter we shall consider equations, in which the independent variable t does not occur explicitly:(2.1) $${\dot x} = f(x)$$A vector equation of the form (2.1) is called autonomous. A scalar equation of order n is often written as(2.2) $$x^{(n)}+ F(x^{(n-1)},“ots ,x)=0$$in which x(k) = dkx/dtk, k = 0,1, …, n, x(0) = xIn characterising the solutions of autonomous equations we shall use three special sets of solutions: equilibrium or stationary solutions, periodic solutions and integral manifolds.