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Melnikov theory for weakly coupled nonlinear RLC circuits

Flaviano Battelli1* and Michal Fečkan23

Author Affiliations

1 Department of Industrial Engineering and Mathematical Sciences, Marche Polytecnic University, Via Brecce Bianche 1, Ancona, 60131, Italy

2 Department of Mathematical Analysis and Numerical Mathematics, Comenius University, Mlynská dolina, Bratislava, 842 48, Slovakia

3 Mathematical Institute of Slovak Academy of Sciences, Štefánikova 49, Bratislava, 814 73, Slovakia

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Boundary Value Problems 2014, 2014:101  doi:10.1186/1687-2770-2014-101

Dedicated to Professor Ivan Kiguradze

Published: 7 May 2014


We apply dynamical system methods and Melnikov theory to study small amplitude perturbation of some coupled implicit differential equations. In particular we show the persistence of such orbits connecting singularities in finite time provided a Melnikov like condition holds. Application is given to coupled nonlinear RLC system.

MSC: 34A09, 34C23, 37G99.

implicit ode; perturbation; Melnikov method; RLC circuits