Abstract
In this chapter we shall consider equations, in which the independent variable t does not occur explicitly:
A vector equation of the form (2.1) is called autonomous. A scalar equation of order n is often written as
in which x(k) = dk x/dtk, k = 0, 1, . . ., n, x(0) = x In characterising the solutions of autonomous equations we shall use three special sets of solutions: equilibrium or stationary solutions, periodic solutions and integral manifolds.
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© 1996 Springer-Verlag Berlin Heidelberg
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Verhulst, F. (1996). Autonomous equations. In: Nonlinear Differential Equations and Dynamical Systems. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61453-8_2
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DOI: https://doi.org/10.1007/978-3-642-61453-8_2
Publisher Name: Springer, Berlin, Heidelberg
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