Self-oscillations in a certain Belousov–Zhabotinsky model

Abstract

We consider the dynamic properties of a system of three differential equations known as the oreganator model. This model depends on four external parameters and describes one of the periodic Belousov–Zhabotinsky reactions. We obtain broad conditions for the parameters that ensure the existence of nonstationary steady-state regimes in oregonator model. With classical values of the parameters, the localization of the limit (at a long time) dynamics in the phase space has been improved. In fact, using numerical analysis, we significantly narrow the bounded region of the phase space containing the trajectories of the system. An iterative procedure is proposed for the approximate localization of closed trajectories (cycles) of the system on algebraic surfaces inR3. A promising problem of theoretical substantiation of the numerical convergence of this procedure is posed.