Two Limit Cycles in a Two-Species Reaction

2018. 09. 27. 10:15
BME H. épület 306-os terem
Ilona Nagy (BME, Department of Analysis)




                 We kindly invite you to the Miklós Farkas Seminar.


                     27 September (Thursday) 10.15, BME H306


                        Ilona Nagy (BME, Department of Analysis)




Two Limit Cycles in a Two-Species Reaction

Kinetic differential equations, being nonlinear, are capable of producing many kinds of exotic phenomena. However, the existence of multistationarity, oscillation or chaos is usually proved by numerical methods. Here we investigate a relatively simple reaction among two species consisting of five reaction steps, one of the third order. About this reaction we show the following facts (using symbolic methods): the kinetic differential equation of the reaction has two limit cycles surrounding the stationary point of focus type in the positive quadrant. The outer limit cycle is always stable and the inner one is always unstable. We also performed the search for partial integrals of the system and have found one such integral. Application of the methods needs computer help (Wolfram language and Singular) because the symbolic calculations to carry out are too complicated to do by hand. Even to make characteristic drawings is very far from trivial: the inner limit cycle is very small. Some of the methods we use are relatively new, and all of them have never been used in reaction kinetics, although they can be used to have similar exact results on other models.


The organizers

(István Faragó, János Karátson, Róbert Horváth, Miklós Mincsovics)