Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 29, Issue 9, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127419300258
Keywords
Reaction-diffusion system; Gierer-Meinhardt model; asymptotic stability; Turing instability; Hopf bifurcation; periodic solutions
Funding
- National Natural Science Foundation of China [61563026]
- Foundation of a Hundred Youth Talents Training Program of Lanzhou Jiaotong University [152022]
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A reaction-diffusion Gierer-Meinhardt system with homogeneous Neumann boundary condition on one-dimensional bounded spatial domain is considered in the present article. Local asymptotic stability, Turing instability and existence of Hopf bifurcation of the constant positive equilibrium are explored by analyzing in detail the associated eigenvalue problem. Moreover, properties of spatially homogeneous Hopf bifurcation are carried out by employing the normal form method and the center manifold technique for reaction-diffusion equations. Finally, numerical simulations are also provided in order to check the obtained theoretical conclusions.
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