Propagation of waves through anharmonic defects: a strongly anharmonic dangling resonator

Delayed differential equation of motion is derived for an anharmonic resonator coupled to a monomode transmission line. Transmission and reflection coefficients are found analytically in the harmonic approximation. Nonlinear response of the system is analysed by an electric circuit obeying the same equations of motion. An aperiodic (chaotic) response is found mainly in the frequency range close to the resonance of the dangling resonator. Zeros of transmission and total transmissions are shown to be destroyed by the anharmonicity nearly in the same frequency region.