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DC Field | Value | Language |
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dc.contributor.author | Winter, M | - |
dc.date.accessioned | 2014-02-17T09:33:16Z | - |
dc.date.available | 2014-02-17T09:33:16Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | SIAM Journal on Mathematical Analysis, 42(6), 2818 - 2841, 2010 | en_US |
dc.identifier.issn | 0036-1410 | - |
dc.identifier.uri | http://epubs.siam.org/doi/abs/10.1137/100792299 | en |
dc.identifier.uri | http://bura.brunel.ac.uk/handle/2438/8027 | - |
dc.description | Copyright @ 2010 Society for Industrial and Applied Mathematics | en_US |
dc.description.abstract | We study a reaction-diffusion system with four morphogens which has been suggested in [H. Takagi and K. Kaneko, Europhys. Lett., 56 (2001), pp. 145–151]. This system is a generalization of the Gray–Scott model [P. Gray and S. K. Scott, Chem. Eng. Sci., 38 (1983), pp. 29–43; 39 (1984), pp. 1087–1097] and allows for multiple activators and multiple substrates. We construct single-spike solutions on the real line and establish their stability properties in terms of conditions of connection matrices which describe the interaction of the components. We use a rigorous analysis for the linearized operator around single-spike solutions based on nonlocal eigenvalue problems and generalized hypergeometric functions. The following results are established for two activators and two substrates: Spiky solutions may be stable or unstable, depending on the type and strength of the interaction of the morphogens. In particular, it is shown that these patterns are stabilized in the following two cases. Case 1: interaction of different activators with each other (off-diagonal interaction of activators). Case 2: variation in strength of interaction of activators with different substrates (e.g., each activator has its preferred substrate). | en_US |
dc.language | English | - |
dc.language.iso | en | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.subject | Pattern formation | en_US |
dc.subject | Stability | en_US |
dc.subject | Spike solutions | en_US |
dc.subject | Reaction-diffusion system | en_US |
dc.subject | Four morphogens | en_US |
dc.title | Stability of spiky solutions in a reaction-diffusion system with four morphogens on the real line | en_US |
dc.type | Article | en_US |
dc.identifier.doi | http://dx.doi.org/10.1137/100792299 | - |
pubs.organisational-data | /Brunel | - |
pubs.organisational-data | /Brunel/Brunel Active Staff | - |
pubs.organisational-data | /Brunel/Brunel Active Staff/School of Info. Systems, Comp & Maths | - |
pubs.organisational-data | /Brunel/Brunel Active Staff/School of Info. Systems, Comp & Maths/Maths | - |
pubs.organisational-data | /Brunel/University Research Centres and Groups | - |
pubs.organisational-data | /Brunel/University Research Centres and Groups/School of Health Sciences and Social Care - URCs and Groups | - |
pubs.organisational-data | /Brunel/University Research Centres and Groups/School of Health Sciences and Social Care - URCs and Groups/Brunel Institute for Ageing Studies | - |
pubs.organisational-data | /Brunel/University Research Centres and Groups/School of Health Sciences and Social Care - URCs and Groups/Centre for Systems and Synthetic Biology | - |
pubs.organisational-data | /Brunel/University Research Centres and Groups/School of Information Systems, Computing and Mathematics - URCs and Groups | - |
pubs.organisational-data | /Brunel/University Research Centres and Groups/School of Information Systems, Computing and Mathematics - URCs and Groups/Brunel Institute of Computational Mathematics | - |
Appears in Collections: | Publications Dept of Mathematics Research Papers Mathematical Sciences |
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