×

zbMATH — the first resource for mathematics

Chaotic behavior in the dynamical system of a continuous stirred tank reactor. (English) Zbl 0623.58035
The dynamical system describing a continuous stirred tank reactor (CSTR) for the reactions \(A\to B\to C\) and \(A\to C\), \(B\to D\) is considered. A circulating attractor with accompanying circulating orbits is shown to exist when the critical point of the system is unique and unstable. The orbit structure has been numerically found to consist of periodic orbits and chaotic behavior.

MSC:
58Z05 Applications of global analysis to the sciences
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
92Exx Chemistry
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Lynch, D.T.; Rogers, T.D.; Wanke, S.E., Mathematical modelling, 3, 103-116, (1982)
[2] Jorgensen, D.V., Dynamics and exotic behavior of a stirred tank reactor, ()
[3] Retzloff, D.G.; Chicone, C., Chem. eng. commun., 12, 365-376, (1981)
[4] Chicone, C.; Retzloff, D.G., Nonlinear analysis, Theory, methods and applications, 6, 983-1000, (1982)
[5] D.G. Retzloff, P.C-H. Chan, R. Mohamed, C. Chicone and D. Offin, to appear in Journal of Mathematical Analysis and Applications. · Zbl 0656.76089
[6] Pikios, C.A.; Luss, D., Chem. eng. sci., 34, 919-927, (1979)
[7] Marsden, J.E.; McCracken, M., The Hopf bifurcation and its applications, (1976), Springer New York · Zbl 0346.58007
[8] J.C. Roux, P. Richetti, A. Arneodo and F. Argoul, Chaos in a chemical system: toward a global interpretation, preprint. · Zbl 0708.92005
[9] Silnikov, L.P., Soc. math. dokl., 6, 163-166, (1965)
[10] Silnikov, L.P., Math. U.S.S.R. sbornik, 10, 91-102, (1970)
[11] Guckenheimer, J.; Holmes, P., Nonlinear oscillations, dynamical systems, and bifurcation of vector fields, (1983), Springer New York · Zbl 0515.34001
[12] Eckman, P., Routes to chaos with special emphasis on period doubling, ()
[13] Benettin, G.; Gulgani, L.; Giorgilli, A.; Strelcyn, J., Meccanica, 9-20, (March 1980)
[14] Benettin, G.; Gulgani, L.; Giorgilli, A.; Strelcyn, J., Meccanica, 21-30, (March 1980)
[15] Shimadu, I.; Magashima, T., Prog. theoretical phys., 61, 1605-1616, (1979)
[16] Lichtenberg, A.J.; Lieberman, M.A., Regular and stochastic motion, (1983), Springer New York · Zbl 0506.70016
[17] Kaplan, J.L.; Yorke, J.A., Chaotic behavior of multidimensional difference equations, (), 204-237
[18] Smale, S., Bull. amer. math. soc., 73, 747-817, (1967)
[19] Palis, J.; deMelo, W., Geometric theory of dynamical systems, (1982), Springer New York
[20] Feigenbaum, M.J., J. stat. phys., 19, 158-185, (1978)
[21] Feigenbaum, M.J., Los alamos science, 1, 4-27, (1980)
[22] Roux, J.C.; Sinoyi, R.H.; Swinney, H.L., Physica, 8D, 257-266, (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.