  In this paper we obtain new complete hybrid formula for corresponding class
of $\zeta$-factorization formulas. We demonstrate that this formula is the
synergetic one. Namely, this one describes the cooperation between some class
of elementary functions and Riemann's zeta-function on a class of disconnected
sets on the critical line. Some comparizon between this pure mathematical
phenomenon and the Belousov-Zhabotinski chemical reaction is added.
  \centering DEDICATED TO 110th ANNIVERSARY OF HARDY'S PURE MATHEMATICS
