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A set of rate constants and two corresponding positive steady states are constructed for each case.
We focus on the asymptotic profile of positive steady state solutions.
The subnetwork analysis provides some sufficient conditions for which a (forest like or circular) reaction network could be determined to have capacity of admitting multiple positive steady states if it contains a subnetwork that also admits multiple positive steady states.
Furthermore, we can obtain that under some conditions, the unique positive steady state solution of the system is globally asymptotically stable.
By bifurcation theorem we obtain one sufficient condition of the existence of nonconstant positive steady state solution in one dimensional case.
S. Akle, O. Dalal, R. M. T. Fleming, M. A. Saunders, N. A. Taheri, and Y. Ye, Existence of positive steady states for mass conserving and mass-action chemical reaction networks with a single terminal-linkage class, arXiv 1106:2359.
Similar(9)
We show that positive steady-state solutions with certain prescribed spatial patterns can be obtained when the spatial environment is designed suitably.
The third is a periodic collection of 'droplet' (compactly supported) steady-states having lower energy than either the positive steady-state or the constant one.
Suppose that ((u(x),v(x))) is any given positive steady-state solution of system (1.2).
Then we show the nonexistence of nonconstant positive steady-state solutions of the system.
The existence and uniqueness of the positive steady-state solution are established under suitable conditions.
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