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Title of article :
The zone boundary mode in periodic nonlinear electrical lattices
Author/Authors :
Bhat، نويسنده , , H.S. and Osting، نويسنده , , B.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2009
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Abstract :
We study the existence and linear stability of the zone boundary mode in a nonlinear electrical lattice consisting of N inductors and N 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 2 N × 2 N 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 − 2 . Numerical computations validate the perturbative results.
Keywords :
Nonlinear transmission lines , Anharmonic lattices , Stability theory , Nonlinear modes , Zone boundary mode
Journal title :
Physica D Nonlinear Phenomena
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