Chattopadhyay, J. ; Tapaswi, P. K. ; Mukherjee, Debasis (1992) Formation of a regular dissipative structure: a bifurcation and nonlinear analysis Biosystems, 26 (4). pp. 211-222. ISSN 0303-2647
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Official URL: http://linkinghub.elsevier.com/retrieve/pii/030326...
Related URL: http://dx.doi.org/10.1016/0303-2647(92)90026-U
Abstract
A non-linear reaction diffusion model of a negative feedback epigenetic control system is presented. The model involves synthesis of the mitotic inducing and inhibiting proteins, simultaneously with intercellular self-diffusion and cross-diffusion of the latter only. The importance of negative cross-diffusion for creating a regular dissipative structure is shown. A bifurcation analysis of the non-linear diffusive system has been performed and it is concluded that bifurcation is supercritical. Lastly, using Liapunov's direct method, it is shown that the pattern evolved by the system is globally asymptotically stable.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Epigenetic system; Negative cross-diffusion; Dissipative structure; Bifurcation analysis; Liapunov stability |
| ID Code: | 7455 |
| Deposited On: | 25 Oct 2010 11:28 |
| Last Modified: | 30 May 2011 06:44 |
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