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Existence and stability of periodic solutions in weakly non‐linear electrical circuits via averaging and functional analytical methods
Author(s) -
Ulmet D. E.
Publication year - 1992
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490200408
Subject(s) - mathematics , electronic circuit , stability (learning theory) , dynamical systems theory , electrical network , exponential stability , invariant (physics) , class (philosophy) , network analysis , linear system , topology (electrical circuits) , mathematical analysis , nonlinear system , computer science , physics , quantum mechanics , machine learning , artificial intelligence , combinatorics , mathematical physics
The method of averaging has been extensively used to detect invariant manifolds for non‐linear dynamical systems. In this paper we combine the averaging analysis with some functional analytical methods to prove the existence and stability of periodic solutions for a class of weakly non‐linear electrical circuits. We also prove a specific averaging theorem for these circuits using Gronwall estimates and the Sanchez‐Palencia summation trick. These results are applied to the model equations of a system of coupled Van der Pol oscillators to obtain the existence of orbitally asymptotically stable periodic solutions. Finally we construct asymptotic approximations of these solutions and perform a numerical simulation of the flow.