Slowly modulated oscillations in nonlinear diffusion processes

Creators: Cohen, Donald S.; Hoppensteadt, Frank C.; Miura, Robert M.

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Abstract

It is shown here that certain systems of nonlinear (parabolic) reaction-diffusion equations have solutions which are approximated by oscillatory functions in the form R(ξ - cτ)P(t^*) where P(t^*) represents a sinusoidal oscillation on a fast time scale t* and R(ξ - cτ) represents a slowly-varying modulating amplitude on slow space (ξ) and slow time (τ) scales. Such solutions describe phenomena in chemical reactors, chemical and biological reactions, and in other media where a stable oscillation at each point (or site) undergoes a slow amplitude change due to diffusion.

Additional Information

© 1977 Society for Industrial and Applied Mathematics. Received by the editors February 11, 1976, and in revised form November 17, 1976. This work was performed at a workshop on Mathematical Problems in Ecology, August, 1975, organized by Professor Donald L. Ludwig, University of British Columbia, and supported by the National Research Council of Canada. [D.S.C. was] [s]upported in part by the U.S. Army Research Office under Contract DAHC-04-68-006 and the National Science Foundation under Grant GP32157X2. [F.C.H. was] [s]upported in part by the U.S. Air Force Scientific Research Office under Grant AFOSR-71-2107 and by the U.S. Army Research Office under Grant DAAG29-74-G-0219. [R.M.M. was] [s]upported in part by the National Science Foundation under Grant GP-34319. The authors gratefully acknowledge the hospitality of Professor Donald L. Ludwig, University of British Columbia, and that of the University of British Columbia.

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