Reaction and diffusion on growing domains: Scenarios for robust pattern formation
We investigate the sequence of patterns generated by a reaction—diffusion system on a growing domain. We derive a general evolution equation to incorporate domain growth in reaction—diffusion models and consider the case of slow and isotropic domain growth in one spatial dimension. We use a self-sim...
| প্রধান লেখক: | , , |
|---|---|
| বিন্যাস: | Journal article |
| প্রকাশিত: |
1999
|
| সংক্ষিপ্ত: | We investigate the sequence of patterns generated by a reaction—diffusion system on a growing domain. We derive a general evolution equation to incorporate domain growth in reaction—diffusion models and consider the case of slow and isotropic domain growth in one spatial dimension. We use a self-similarity argument to predict a frequency-doubling sequence of patterns for exponential domain growth and we find numerically that frequency-doubling is realized for a finite range of exponential growth rate. We consider pattern formation under different forms for the growth and show that in one dimension domain growth may be a mechanism for increased robustness of pattern formation. |
|---|