Modulated waves and chaotic-like behaviours in the discrete electrical transmission line

The dynamics of a weakly nonlinear modulated wave in a discrete electrical transmission line with negative nonlinear resistance and dissipative effects is investigated. This leads to the propagation of envelope modulation in the line modelled by the discrete complex Ginzburg?Landau equation. For an initial modulated plane wave propagating in the line, the criteria for modulational instability as well as the threshold amplitude are derived. The evolution of modulated waves which have the shape of an envelope soliton and the chaotic-like behaviour of the system are also examined. We show that dissipation can affect patterns propagating into the system. Numerical simulations demonstrate the validity of theoretical predictions.