Application Of Non-Linear Differential Equations In Auto-Catalytic Chemical Kinetics

Abstract

In this study,we have considered the stability nature of a two dimensional non-linear differentialequation,popularlyknownastheBrusselatormodelandanalysisdynamicalbehavior of the model.The stability of Brusselator model with parameters a and b depend on the concentration chemical corresponding initial conditions is stable if b > a2 +1. So that stability analysis of the equilibrium point of the modified model had be done using Jacobian matrix orRouth-HurwitzCriteria. WejustifytheexistenceofHopfbifurcationinatwodimensional nonlinear differential equation with the help of Hopf bifurcation theorem and technique of Normal forms to show that supercritical Hopf bifurcation occurs in the system we have considered.The stability of new system formed by hypothesis b kept constantly injected into system with rate v is stable v < 1.21922,besides to all concentration tend toward critical point otherwiseitsunstableandconcentrationremainsboundedorunboundedtolargelineswhile concentrationof x goestozero.ThenumericalsolutionsofthesystemofnonlinearDEswas supplemented by using the built ode45 Mathlab software.