A Survey on the Melnikov Theory for Implicit Ordinary Differential Equations with Applications to RLC Circuits

DOI10.1007/978-3-030-12232-4_4zbMath1430.34012OpenAlexW2921038746MaRDI QIDQ5215341

Michal Fečkan

Publication date: 10 February 2020

Published in: Studies in Systems, Decision and Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-12232-4_4

zbMATH Keywords

RLC circuitsimpasse pointsimplicit ordinary differential equationsIK-singularities

Mathematics Subject Classification ID

Implicit ordinary differential equations, differential-algebraic equations (34A09) Analytic circuit theory (94C05) Applications of operator theory in systems, signals, circuits, and control theory (47N70) Nonautonomous smooth dynamical systems (37C60) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02)

Related Items (1)

Multiple anti-periodic solutions of implicit differential inclusions on tori

Cites Work

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• Generalized inverse operators and Fredholm boundary-value problems. Translated from the Russian by P. V. Malyshev
• Blue sky-like catastrophe for reversible nonlinear implicit ODEs
• Melnikov theory for weakly coupled nonlinear RLC circuits
• Exponential dichotomies, heteroclinic orbits, and Melnikov functions
• A general existence and uniqueness theory for implicit differential- algebraic equations
• Homoclinic period blow-up in reversible and conservative systems
• Boundary value problems for systems of implicit differential equations
• On impasse points of quasilinear differential-algebraic equations
• A geometric treatment of implicit differential-algebraic equations
• Implicit differential equations near a singular point
• Exponential dichotomies and transversal homoclinic points
• On the existence of solutions connecting singularities in nonlinear RLC circuits
• Nonlinear RLC circuits and implicit ODEs.
• On the existence of solutions connecting IK singularities and impasse points in fully nonlinear RLC circuits
• Melnikov theory for nonlinear implicit ODEs
• On the Computation of Impasse Points of Quasi-Linear Differential-Algebraic Equations
• Peano's theorem for implicit differential equations

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