Forced Oscillations of a Self-Oscillating Bimolecular Surface Reaction Model

Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota, 55455, U.S.A. 

The effects of forced oscillations in the partial pressure of a reactant is studied in a simple isothermal, bimolecular surface reaction model in which two vacant sites are required for reaction. The forced oscillations are conducted in a region of parameter space where an autonomous limit cycle is observed, and the response of the system is characterized with the aid of the stroboscopic map where a two-parameter bifurcation diagram for the map is constructed by using the amplitude and frequency of the forcing as bifurcation parameters. The various responses include subharmonic, quasi-peri-odic, and chaotic solutions. In addition, bistability between one or more of these responses has been observed. Bifurcation features of the stroboscopic map for this system include folds in the sides of some resonance horns, period doubling, Hopf bifurcations including hard resonances, homoclinic tangles, and several different codimension-two bifurcations. 

Forced oscillation is a well-known technique for the characterization of linear systems and is referred to as a frequency response method in the process control field. By contrast, the response of nonlinear systems to forcing is much more diverse and not yet fully understood. In nonlinear systems, the forced response can be periodic with a period that is some integer multiple of the forcing period (a subharmonic response), or quasi-periodic (characterized by more than one frequency) or even chaotic, when the time series of the response appears to be random. In addition, abrupt transitions or bifurcations can occur between any of these responses as one or more of the parameters is varied and there can be more than one possible response for a given set of parameters depending on the initial conditions or recent history of the system. 

Before such process control strategies can be implemented, either for 

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McKarnin, M. A., Schmidt, L. D., and Aris, R. (1988). Forced oscillations of a self-oscillating bimolecular surface reaction model. Proc. R. Soc., A417, 363-88. 

A comparative study was done by Kevrekidis and published as I. G. Kevrekidis, L. D. Schmidt, and R. Aris. Some common features of periodically forced reacting systems. Chem. Eng. Sci. 41,1263-1276 (1986). See also two papers by the same authors Resonance in periodically forced processes Chem. Eng. Sci. 41, 905-911 (1986) The stirred tank forced. Chem. Eng. Sci. 41,1549-1560 (1986). A full study of the Schmidt-Takoudis vacant site mechanism is to be found in M. A. McKamin, L. D. Schmidt, and R. Aris. Autonomous bifurcations of a simple bimolecular surface-reaction model. Proc. R. Soc. Lond. A 415,363-387 (1988) Forced oscillations of a self-oscillating bimolecular surface reaction model. Proc. R. Soc. Lond. A 415,363-388 (1988). 

L. Forced Oscillations of a Self-Oscillating Bimolecular Surface Reaction Model... 

FORCED OSCILLATIONS OF A SELF-OSCILLATING BIMOLECULAR SURFACE REACTION MODEL... 

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