Stability analysis of Turing patterns generated by the Schnakenberg model
Copyright policy )Stability analysis of Turing patterns generated by the Schnakenberg model
We consider the following Schnakenberg model on the interval (-1,1): [formula see text] where D1 > 0, D2 > 0, B > 0. We rigorously show that the stability of symmetric N-peaked steady-states can be reduced to computing two matrices in terms of the diffusion coefficients D1, D2 and the number N of peaks. These matrices and their spectra are calculated explicitly and sharp conditions for linear stability are derived. The results are verified by some numerical simulations.
- Chinese University of Hong Kong China (People's Republic of)
- University of Stuttgart Germany
- Brunel University London United Kingdom
- University of California, Irvine United States
PDEs in connection with biology, chemistry and other natural sciences, Turing instability, symmetric \(N\)-peaked solutions, nonlocal eigenvalue problem, Models, Biological, 510, Pattern Recognition, Automated, Diffusion, Solutions, Kinetics, Nonlocal Eigenvalue Problem, Spectral theory and eigenvalue problems for partial differential equations, Developmental biology, pattern formation, Symmetric N-peaked solutions, Mathematics
PDEs in connection with biology, chemistry and other natural sciences, Turing instability, symmetric \(N\)-peaked solutions, nonlocal eigenvalue problem, Models, Biological, 510, Pattern Recognition, Automated, Diffusion, Solutions, Kinetics, Nonlocal Eigenvalue Problem, Spectral theory and eigenvalue problems for partial differential equations, Developmental biology, pattern formation, Symmetric N-peaked solutions, Mathematics
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