The buffer phenomenon in an RCLG oscillator: Theoretical analysis and experimental results (Q2784574)

The paper deals with partial differential equations like NEWLINE\[NEWLINE u_t=-v_x-\alpha_1u,\quad v_t=-u_x-\alpha_2v\tag{1}NEWLINE\]NEWLINE NEWLINE\[NEWLINEv|_{x=1}=0,\quad u|_{x=0}+\beta_0u|_{x=1}+\beta_1u^2|_{x=1}-\beta_2u^3|_{x=1}=0,NEWLINE\]NEWLINE which describes the operation of an RCLG oscillator with an ideal amplifier and with distributed parameters. The infinite-dimensional normalization method is used which is a special version of the Krylov-Bogolyubov-Mitropol'skij asymptotic method. It is shown that, under suitable choice of parameters, system (1) has an arbitrarily given number of small stable cycles. This is the so-called buffer phenomenon. The evolution of those cycles is discussed as parameters increase for predicting discontinuous oscillations in (1). Theoretical results are compared with experimental observations.NEWLINENEWLINEFor the entire collection see [Zbl 0983.00023].