Melnikov theory for weakly coupled nonlinear RLC circuits
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
Boundary Value Problems 2014, 2014:101 doi:10.1186/1687-2770-2014-101
Dedicated to Professor Ivan KiguradzePublished: 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.