2023/10/01 by Hewan Shemtaga, Wenxian Shen, Shemtaga, Hewan +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #35P05 #35Q92 #92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical Biology Tumor Growth #Mathematical and Theoretical Epidemiology and Ecology Models #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2310.00756
openalex publication_date 2023/10/01 · openalex created_date 2023/10/04 · openalex updated_date 2026/07/28
This paper concerns asymptotic stability, instability, and bifurcation of constant steady state solutions of the parabolic-parabolic and parabolic-elliptic chemotaxis models on metric graphs. We determine a threshold value χ^*>0 of the chemotaxis sensitivity parameter that separates the regimes of local asymptotic stability and instability, and, in addition, determine the parameter intervals that facilitate global asymptotic convergence of solutions with positive initial data to constant steady states. Moreover, we provide a sequence of bifurcation points for the chemotaxis sensitivity parameter that yields non-constant steady state solutions. In particular, we show that the first bifurcation point coincides with threshold value χ^* for a generic compact metric graph. Finally, we supply numerical computation of bifurcation points for several graphs.