The bifurcation analysis and chaos anti-control of a differential-algebraic system

In this paper, the nonlinear and linear mathematical model of a Continuous Stirred Tank Reactor (CSTR) where an irreversible exothermic reaction takes place is considered. Then a differential-algebraic system (DAS) is established for such an irreversible exothermic reaction. We analyze the stability and the bifurcation of the differential-algebraic system. Chaos is not only useful but also very desirable in fluid mixing. If the dynamics of the particle motion in the two fluids are strongly chaotic, two fluids can be thoroughly mixed and the consumed energy is minimized. For this reason, an adaptive controller is designed to make the DAS chaotic. Numerical simulations are performed to illustrate the analytical results.