Stability and Bifurcation Analysis of Activator-inhibitor Reaction Diffusion System

Abstract

In this thesis, stability and bifurcation analysis of activator-inhibitor reaction diffusion system was considered. The system was analyzed into two parts. The first part is without diffusion. Without diffusion, the system was linearized using Jacobean matrix about equilibrium point. The local stability condition of the equilibrium point was proved by using Routh Hurwitz stability criteria. Hopf bifurcation condition without diffusion was determined by the help of Hopf bifurcation theorem in planar system. The second part is with diffusion. With diffusion, stability conditions are proved by using Routh Hurwitz stability criteria. Diffusive instability condition was also set down. The system undergoes Hopf bifurcation with diffusion provided that specific condition is satisfied. Finally, in order to verify the applicability of the result two numerical examples were solved and MATLAB simulation was implemented to support the findings of the study.