Article ID Journal Published Year Pages File Type
1897583 Physica D: Nonlinear Phenomena 2009 13 Pages PDF
Abstract

We study the existence and linear stability of the zone boundary mode in a nonlinear electrical lattice consisting of NN inductors and NN voltage-dependent capacitors with periodic boundary conditions. The inductances are allowed to alternate, while the capacitors are identical and each have a quadratic dependence on voltage. By block-diagonalizing a 2N×2N2N×2N Floquet problem, we reduce the question of the stability of the mode to a single Hill’s equation that is analyzed using methods of perturbation theory and averaging. We show that periodicity of the lattice inductances degrades stability, and also show that the instability threshold is proportional to N−2N−2. Numerical computations validate the perturbative results.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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