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On biological pattern formation by contact inhibition

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1 Author(s)
Arcak, M. ; Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, CA, USA

Many patterning events in multi-cellular organisms rely on cell-to-cell contact signaling. We study a model which employs a graph to describe which cells are in contact, and examine its spatio-temporal dynamics. We first give an instability condition for the homogeneous steady-state. We then show that, for bipartite graphs, this instability condition also guarantees the existence and asymptotic stability of steady-states that exhibit a pattern of alternating high and low values in adjacent cells. Finally, we establish a strong monotonicity property of this model for bipartite graphs, which implies that almost every bounded solution converges to a steady-state.

Published in:

American Control Conference (ACC), 2012

Date of Conference:

27-29 June 2012