Bifurcation Behaviors of Steady-State Solution to a Discrete General Brusselator Model

Abstract EN

We study the local and global bifurcation of nonnegative nonconstant solutions of a discrete general Brusselator model.

We generalize the linear u in the standard Brusselator model to the nonlinear fu.

Assume that f∈C0,∞,0,∞ is a strictly increasing function, and f′f−1a∈0,∞.

Taking b as the bifurcation parameter, we obtain that the solution set of the problem constitutes a constant solution curve and a nonconstant solution curve in a small neighborhood of the bifurcation point b0j,f−1a,ab/f−1a2.

Moreover, via the Rabinowitz bifurcation theorem, we obtain the global structure of the set of nonconstant solutions under the condition that fs/s2 is nonincreasing in 0,∞.

In this process, we also make a priori estimation for the nonnegative nonconstant solutions of the problem.