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Hopf Bifurcation in a Reaction-Diffusion
Nor Azua Ilyani Binti Mohd Shukri
Supervisor: Assoc. Prof Dr. Zabidin Bin Salleh
Bachelor of Science (Financial Mathematics)
School of Informatics and Applied Mathematics
In this research, we want to determine the Hopf bifurcation in a reaction-diffusion. There
are many objectives which contribute of study regarding to the Hopf bifurcation in a
reaction-diffusion. Some method was used to determine the Hopf bifurcation in a
reaction-diffusion. For the ordinary differential equation (ODE) system, the method of
Taylor Expansion and Poincare Andronov-Hopf were used. Next, for the partial differential
equations (PDE) system, the method of the normal form and center manifold theorem
were used. We also applied the equilibrium point, the stability of the periodic solutions
and the direction of the Hopf bifurcation in this system. Thus the result for the equilibrium
point of the system is stable or unstable based on the property changes when the
parameter c towards to the fix C 0 while the result for the direction of Hopf bifurcation is
supercritical and the bifurcating periodic solution are unstable.
844 | UMT UNDERGRADUATE RESEARCH DAY 2018