Analysis Dynamics In The Belousov-Zhabotinsky Reaction

The nonlinear phenomena of a chemical model are discussed in theBelousov-Zhabotinsky(BZ) oscillation reaction system by applyingqualitative theory and stability theory of differential equations, the centermanifold theorem, local bifurcations and the method of higher orderharmonic balance, etc. The existence and stability of the equilibriumpoints and their local bifurcations are investigated, especially, theexistence of Hopf bifurcations of the equilibrium points for the system isanalyzed by using Hopf bifurcation theory in time domain and infrequency domain, which causes the oscillation phenomena in thesereactions; and the second-order harmonic balance approximation is usedto estimate the frequency, amplitude and the approximate analyticalexpression of the limit cycles generated by the Hopf bifurcation. Theresults of theoretical analysis are verified and new complex phenomenaare revealed, such as period doubling oscillations and chaos, by means ofnumerical simulation.In this paper, there are five chapters. In chapter1, the research background of the nonlinear science is introduced, together with researchprogress and application of BZ oscillation reaction in details.In chapter2, a brief review is presented, which includes thedynamical systems theory—the center manifold theorem, localbifurcations, Hopf bifurcation in frequency domain and the rules of limitcycle stability.In chapter3, a BZ oscillation reaction model—Montanator model isselected to study its dynamic. The existence, stability, bifurcations of theequilibrium points are discussed when the flow rate as the bifurcationparameter. We prove that a supercritical Hopf point can occur in thesystem, which causes oscillation. Meanwhile, there exists a subcriticalHopf point in the system. We also study the influence of the reaction rateconstant (k6) on the dynamical behavior and have a conclusion that thesystem has two subcritical Hopf points. Besides, the theoretical analysisresults are verified via numerical simulation, and the simple oscillation,periodic-2oscillation, periodic-4oscillation and chaos are found.In chapter4, Hopf bifurcation theory in the frequency domain andsecond-order harmonic balance approximation are used to estimate thefrequency, amplitude and approximate analytical expression of the limitcycles generated by the Hopf bifurcation by adjusting some parameters inthe model. The stability of the limit cycle is analyzed by using the rulesof stability of limit cycle. In chapter5, the research work is summarized, and we also discussthe next reach.