Differential and Integral Equations

Nonlinear RLC Circuits and Implicit ODEs

Flaviano Battelli and Michal Fečkan

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We apply dynamical system methods and Melnikov theory to study small amplitude perturbation of some implicit differential equations exhibiting I--singularities (in the sense given in [16, p. 166]). In particular, we show persistence of such I-singularities and orbits connecting them in finite time provided a Melnikov like condition holds. We start from a concrete example where, we prove that this Melnikov condition actually holds. Then, we extend our results to more general implicit differential equations.

Article information

Differential Integral Equations, Volume 27, Number 7/8 (2014), 671-690.

First available in Project Euclid: 6 May 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34A09: Implicit equations, differential-algebraic equations [See also 65L80] 34C23: Bifurcation [See also 37Gxx] 37G99: None of the above, but in this section


Battelli, Flaviano; Fečkan, Michal. Nonlinear RLC Circuits and Implicit ODEs. Differential Integral Equations 27 (2014), no. 7/8, 671--690. https://projecteuclid.org/euclid.die/1399395748

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