perturbation theory

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perturbation theory

[‚pər·tər′bā·shən ‚thē·ə·rē]
(mathematics)
The study of the solutions of differential and partial differential equations from the viewpoint of perturbation of solutions.
(physics)
The theory of obtaining approximate solutions to the equations of motion of a physical system when these equations differ by a small amount from equations which can be solved exactly.
References in periodicals archive ?
Via a blow up we establish a bridge between non-smooth dynamical systems and the geometric singular perturbation theory.
The paper is organized as follows: in Section 2 we give the basic theory about Non-Smooth Vector Fields on the plane, in Section 3 we give the theory about the regularization process, in Section 4 we present a few relevant methods of Geometric Singular Perturbation Theory, in Section 5 we present the singularities treated in Theorem 1, give its topological normal forms and prove Theorem 1, in Section 6 we present the singularities treated in Theorem 2, give its topological normal forms and prove Theorem 2.
The understanding of the phase portrait of the vector field associated to a SP-problem is the main goal of the geometric singular perturbation theory.
Algebraic analysis of singular perturbation theory.
Nearly twenty years later, Szmolyan and Wechselberger [5] extended "Geometric Singular Perturbation Theory (see Fenichel [6, 7], O'Malley [8], Jones [9], and Kaper [10])" to canards problems in [R.
According to the Geometric Singular Perturbation Theory, the zero-order approximation in [epsilon] of the slow manifold associated with the Hodgkin-Huxley model (60a,60b), (60c), and (60d) is obtained by posing [epsilon] = 0 in (60c) and (60d).