Journal
JOURNAL OF MATHEMATICAL CHEMISTRY
Volume 52, Issue 10, Pages 2570-2580Publisher
SPRINGER
DOI: 10.1007/s10910-014-0401-6
Keywords
Lengyel-Epstein System; Bautin bifurcation; First and second Lyapunov coefficients; Normal forms; Hopf and double limit cycle bifurcations
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In this paper, complete analysis is presented to study Bautin bifurcation for the Lengyel-Epstein System {du/dt = a - u - 4uv/1+u(2), dv/dt = sigma b(u - uv/1+u(2)) Sufficient conditions for a and b are given for the system to demonstrate Bautin bifurcation. By using b and alpha = a/5 as bifurcation parameters and computing the first and second Lyapunov coefficients and performing nonlinear transformation, the normal form with unfolding parameters is derived to obtain the bifurcation diagrams such as Hopf and double limit cycle bifurcations. An example is given to confirm that the system has two limit cycles.
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