Forced oscillations in an exothermic chemical reaction. (English) Zbl 0822.34034
Summary: We study nonlinear behaviour in a model chemical reaction scheme (proposed by Sal’nikov), in which a single chemical species undergoes a two-stage, first-order decay process. The second stage is exothermic and has a temperature-dependent rate, and as a result, spontaneous oscillations in the temperature and the concentration of an intermediate chemical are known to be possible. An additional oscillation is imposed on the system by varying the ambient temperature in a sinusoidal manner.
Primary resonance occurs when the forcing frequency coincides with the frequency of the natural oscillations in this scheme and an infinite sequence of super- and subharmonic resonances is also present. Chaos is possible for appropriate parameter values and may result either from the Feigenbaum period-doubling cascade, or else as a result of the Ruelle- Takens approach through quasi-periodicity.
Primary resonance occurs when the forcing frequency coincides with the frequency of the natural oscillations in this scheme and an infinite sequence of super- and subharmonic resonances is also present. Chaos is possible for appropriate parameter values and may result either from the Feigenbaum period-doubling cascade, or else as a result of the Ruelle- Takens approach through quasi-periodicity.
MSC:
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 92E20 | Classical flows, reactions, etc. in chemistry |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C25 | Periodic solutions to ordinary differential equations |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
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