Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 26, Issue 4, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127416500668
Keywords
Depletion model; asymptotic stability; steady-state bifurcation; numerical simulation
Funding
- National Natural Science Foundation of China [11271236, 11571274]
- Natural Science Basic Research Plan in Shaanxi Province of China [2015JQ1023]
- Industrial Research Project of Science and Technology in Shaanxi Province [2015GY016]
- Fundamental Research Funds for the Central Universities [GK201302025]
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A two-species biological depletion model in a bounded domain is investigated in which one species is a substrate and the other is an activator. Firstly, under the no-flux boundary condition, the asymptotic stability of constant steady-states is discussed. Secondly, by viewing the feed rate of the substrate as a parameter, the steady-state bifurcations from constant steady-states are analyzed both in one-dimensional kernel case and in two-dimensional kernel case. Finally, numerical simulations are presented to illustrate our theoretical results. The main tools adopted here include the stability theory, the bifurcation theory, the techniques of space decomposition and the implicit function theorem.
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