Dynamics and Hopf Bifurcation of a Chaotic Chemical Reaction Model

Abstract

Taking into account an ideal mixture and a well-stirred reactor, some dynamical aspects for a 3-dimensional chaotic system are carried out. Positivity and boundedness of solutions are discussed. Equilibria are investigated and method of linearization is implemented for asymptotic behavior of system about these equilibria. Lyapunov function is constructed to prove the global stability of positive equilibrium point. Moreover, it is proved that system undergoes Hopf bifurcation about its interior (positive) equilibrium. An explicit criterion of Hopf bifurcation without finding the eigenvalues is used for the existence of Hopf bifurcation. Numerical simulation is presented for the illustration of theoretical discussion. Lyapunov dimension is approximated and maximum Lyapunov characteristic exponents are plotted to ensure the chaotic behavior of the model.