Existence and stability of nonconstant positive steady states of morphogenesis models. (21st October 2014)

• Record Type: Journal Article
• Authors: Chen, Haohao; Tong, Bo; Wang, Qi
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 17(2015:Nov. 30)
• Page Start: 3833
• Page End: 3850
• Publication Date: 2014-10-21
• Subjects: steady state -- morphogenesis -- stability; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3321
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we study a one‐dimensional morphogenesis model considered by C. Stinner et al . (Math. Meth. Appl. Sci.2012;35: 445–465). Under homogeneous boundary conditions, we prove the existence of nonconstant positive steady states through local bifurcation theories. Then we rigorously study the stability of these nonconstant solutions when the sensitivity functions are chosen to be linear and logarithmic, respectively. Finally, we present numerical solutions to illustrate the formation of stable inhomogeneous spatial patterns. Our numerical simulations show that this model can develop very complicated and interesting structures even over one‐dimensional finite domains. Copyright © 2014 John Wiley & Sons, Ltd.