Coupled reaction-diffusion 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 studying only stationary solution branches at small lengths, to predict the complex structure of steady-state bifurcations occuring at large system lengths without actually computing this structure. This technique is applicable to arbitrary isothermal or nonisothermal systems of coupled reaction-diffusion equations 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 of describing 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.
All Science Journal Classification (ASJC) codes
- Chemical Engineering(all)
- Industrial and Manufacturing Engineering