Abstract
This paper is devoted to the study of local controllability of chemical reactions. After a brief introduction we give a sufficient condition of local controllability of chemical reactions. We show the use of our condition on a series of examples. In the last section we mention some unsolved problems.
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References
J. Deák, J. Tóth and B. Vizvári, Conservation of matter in complex chemical mechanisms, Alkalmaz. Mat. Lapok 16 (1992) 73–97 (in Hungarian).
P. Érdi and J. Tóth, Mathematical Models of Chemical Reactions. Theory and Applications of Deterministic and Stochastic Models (Princeton University Press, Princeton, 1989).
M. Feinberg and F.J.M. Horn, Dynamics of open chemical systems and the algebraic structure of the underlying reaction network, Chem. Eng. Sci. 29 (1974) 775–787.
I. Lengyel and I.R. Epstein, Modeling of Turing structures in the chlorite–iodide–malonic acid–starch reaction system, Science 251 (1991) 650–652.
V.N. Orlov and L.I. Rozonoer, The macrodynamics of open systems and the variational principle of the local potential II, J. Franklin Inst. 318 (1984) 315–347.
V. Petrov, J. Masere, V. Gápár and K. Showalter, Controlling chaos in the Belousov–Zhabotinsky reaction, Nature 361 (1993) 240–243.
V. Ramakrishna, M.V. Salapka, M. Dahleh, H. Rabitz and A. Peirce, Controllability of molecular systems, Phys. Rev. A 51(2) (1995).
N. Samardzija, Qualitative and control behavior of a class of chemical and biological systems, in: Nonlinear Control Systems Design, ed. A. Isidori (IFAC–Pergamon Press, Oxford, 1989) pp. 351–355.
P.L. Simon, Globally attracting domains in two-dimensional reversible chemical dynamical systems, Ann. Univ. Sci. Budapest. Sect. Comput. 15 (1995) 179–200.
Z. Varga, On controllability of Fisher' model of selection, in: Differential Equations, eds. C.M. Dafermos, G. Ladas and G. Papanicolaou (Marcel Dekker, New York, 1989) pp. 717–723.
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Farkas, G. Local controllability of reactions. Journal of Mathematical Chemistry 24, 1–14 (1998). https://doi.org/10.1023/A:1019150014783
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DOI: https://doi.org/10.1023/A:1019150014783