THE CHAOS SYNCHRONIZATION OF A SINGULAR CHEMICAL MODEL AND A WILLIAMOWSKI–ROSSLER MODEL

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. In order to make the consumed energy minimized, a Willamowski-Rössler model is used to make differential-algebraic system reach chaos synchronization. Numerical simulations are performed to illustrate the analytical results.

[1]  J. E. Cuthrell,et al.  Simultaneous optimization and solution methods for batch reactor control profiles , 1989 .

[2]  S. Levin,et al.  Dynamical behavior of epidemiological models with nonlinear incidence rates , 1987, Journal of mathematical biology.

[3]  David G. Luenberger,et al.  Time-invariant descriptor systems , 1978, Autom..

[4]  L. Olsen,et al.  Chaos versus noisy periodicity: alternative hypotheses for childhood epidemics. , 1990, Science.

[5]  Hariharan Krishnan,et al.  Tracking in Control Systems Described by Nonlinear Differential-Algebraic Equations with Applications to Constrained Robot Systems , 1993, 1993 American Control Conference.

[6]  H. Rosenbrock.  Structural properties of linear dynamical systems , 1974 .

[7]  J. Ottino.  The Kinematics of Mixing: Stretching, Chaos, and Transport , 1989 .

[8]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[9]  F J Muzzio,et al.  Chaos, Symmetry, and Self-Similarity: Exploiting Order and Disorder in Mixing Processes , 1992, Science.

[10]  J. E. Cuthrell,et al.  On the optimization of differential-algebraic process systems , 1987 .

[11]  Sahjendra N. Singh,et al.  Feedback linearization of differential-algebraic systems and force and position control of manipulators , 1993, 1993 American Control Conference.

[12]  Hariharan Krishnan,et al.  On Control Systems Described by a Class of Linear Differential-Algebraic Equations: State Realizations and Linear Quadratic Optimal Control , 1990, 1990 American Control Conference.