Eur. Phys. J. B 32, 73-79 (2003)
https://doi.org/10.1140/epjb/e2003-00075-9

Propagation of waves and chaos in transmission line with strongly anharmonic dangling resonator

¹ The H. Niewodniezański Institute of Nuclear Physics, ul. Radzikowskiego 152, 30-342 Kraków, Poland
² Laboratoire de Dynamique et Structure des Matériaux Moléculaires (CNRS ESA 8024) , UFR de Physique, Université de Lille I, 59655 Villeneuve d'Ascq Cedex, France
³ Department of Electronics, Academy of Mining and Metallurgy, Al. Mickiwicza 30, 30-059, Kraków, Poland

Corresponding author: ^a Piotr.Zielinski@ifj.edu.pl

Received: 14 March 2002
Revised: 25 November 2002
Published online: 14 March 2003

Abstract

Delayed differential equation of motion with multiple lags is derived for an anharmonic stub 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. Enhanced second harmonic generation is found at the frequencies, which in the harmonic approximation correspond to the zeros of transmission. 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 lifted by the anharmonicity nearly in the same frequency region. Higher harmonics are preferentially transmitted at the zero transmission points in the presence of anharmonicity.