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Predicting pattern formation in coupled reaction—diffusion systems

✍ Scribed by Ioannis G. Kevrekidis; Harry S. Brown

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
899 KB
Volume
44
Category
Article
ISSN
0009-2509

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✦ Synopsis

Coupled reaction4iffusion

equations are known to exhibit a wealth of multiple coexisting stationary solution patterns as the characteristic length of the system grows. We describe and implement a technique which allows us. by studymg only stationary solution branches at small system lengths, to predict the complex structure of steady-state bifurcations occurring at large system lengths without actually computing this structure. This technique is applicable to arbitrary isothermal or nonisothermal systems of coupled reaction-StTusion equations with periodic or no-flux boundary conditions.

To illustrate it we use a standard literature example (the Brussellator), where. by computing only the first two solution branches, we accurately predict the steady-state bifurcation structure reported up to much larger system lengths. This technique also provides a compact way ofdescribing and comparing stationary pattern formation in a large class of systems, extending beyond coupled reaction-diffusion equations. We demonstrate this by comparing stationary pattern formation for our test problem (the Brussellator), with the formation of complex surface wave patterns in thin liquid film flow.

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