Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 25, Issue 10, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127415300268
Keywords
Activator-inhibitor model; Hopf bifurcation; steady state bifurcation; Turing instability; asymptotic behavior
Funding
- State Key Program of National Natural Science Foundation of China [11032009]
- Program for New Century Excellent Talents in University [NCET-11-0385]
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In this paper, a diffusive activator-inhibitor model in vascular mesenchymal cells is considered. On one hand, we investigate the stability of the equilibria of the system without diffusion. On the other hand, for the unique positive equilibrium of the system with diffusion the conditions ensuring stability, existence of Hopf and steady state bifurcations are given. By applying the center manifold and normal form theory, the normal forms corresponding to Hopf bifurcation and steady state bifurcation are derived explicitly. Numerical simulations are employed to illustrate where the spatially homogeneous and nonhomogeneous periodic solutions and the steady states can emerge. The numerical results verify the obtained theoretical conclusions.
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