CHEMICAL REACTION SYSTEMS WITH A HOMOCLINIC BIFURCATION: AN INVERSE PROBLEM
Main Article Content
Abstract
A framework for inverse problems is offered to build reaction systems with specified features. The framework includes the definition and analysis of kinetic transformations, which enable the mapping of any polynomial ordinary differential equation to the one that may be represented as a reaction network. The framework is applied to the design of certain bistable reaction systems in two and three dimensions that experience a supercritical homoclinic bifurcation, and the phase spaces' topology is examined.
Downloads
Metrics
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Licensing
TURCOMAT publishes articles under the Creative Commons Attribution 4.0 International License (CC BY 4.0). This licensing allows for any use of the work, provided the original author(s) and source are credited, thereby facilitating the free exchange and use of research for the advancement of knowledge.
Detailed Licensing Terms
Attribution (BY): Users must give appropriate credit, provide a link to the license, and indicate if changes were made. Users may do so in any reasonable manner, but not in any way that suggests the licensor endorses them or their use.
No Additional Restrictions: Users may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
References
Feinberg, M. Lectures on Chemical Reaction Networks, (Delivered at the Mathematics Research
Center, U. of Wisconsin, 1979).
Erdi, P., T´oth, J. ´ Mathematical Models of Chemical Reactions. Theory and Applications of
Deterministic and Stochastic Models. Manchester University Press, Princeton University Press, 1989.
Szili, L., T´oth, J, 1997. On the origin of Turing instability. Journal of Mathematical Chemistry,
: 39–53.
H´ars, V., T´oth, J., 1981. On the inverse problem of reaction kinetics. Qualitative Theory of
Differential Equations, eds. Farkas, M., Hatvani, L., 363–379. 2
T´oth, J., H´ars, V., 1986. Orthogonal transforms of the Lorenz- and R¨ossler- equation. Physica
D, 135–144.
Escher, C., 1981. Bifurcation and coexistence of several limit cycles in models of open
twovariable quadratic mass-action systems. Chemical Physics, 63: 337–348.
Chellaboina, V., Bhat, S. P., Haddad, W. M., Bernstein, D.S., 2009. Modeling and Analysis of
Mass-Action Kinetics. IEEE Control Systems Magazine, 29: 60–78.
Craciun, G., Pantea, C., 2008. Identifiability of chemical reaction networks. Journal of
Mathematical Chemistry, 44: 244–259.
Szederknyi, G., Hangos, K. M., Pni, T., 2011. Maximal and minimal realizations of reaction
kinetic systems: computation and properties. MATCH Communications in Mathematical and in
Computer Chemistry, 65(2): 309–332.
Samardzija, N., Greller, L. D., Wasserman, E., 1989. Nonlinear chemical kinetic schemes derived
from mechanical and electrical dynamical systems. Journal of Chemical Physics, 90: 2296–2304.
Klonowski, W., 1983. Simplifying principles for chemical and enzyme reaction kinetics.
Biophysical Chemistry, 18(3): 73–87.
Okni´nski, A. Catastrophe Theory: Volume 33. Elsevier Science, 1992.
Pantea, C., Gupta, A., Rawlings, J. B., Craciun, G., 2014. The QSSA in chemical kinetics: as
taught and as practiced. Discrete and Topological Models in Molecular Biology, pp. 419–442.
Springer, Berlin.
Hangos, K. M, Szederk´enyi, G., 2011. Mass action realizations of reaction kinetic system
models on various time scales. Journal of Physics: Conference Series, 268.
Hangos, K. M, 2010. Engineering model reduction and entropy-based Lyapunov functions in
chemical reaction kinetics. Entropy 12, pp. 772–797.