The size of the Limit cycles begins small, grows to a As the solution switchesįrom stable solutions to Limit Cycles back to stable solutions, Solutions converge rapidly (R=0.35, transition at 0.41).Ĭlose to the transition points the solutions converge more Note that far away from the transition points the There are 6 plots corresponding to 6 values of b. The Hopf bifurcations occur at approximately The appearance and disappearance of a periodic orbit through a localĬhange in the stability properties of a steady point is known as a Solution is a limit cycle (Blue circles). Where LC is small, the solution has a stable Y and the product, LC, was plotted as a function ofī. Of the solutions were calculated for X and Nullclines are plotted in dashed red (dx/dt=0) In a chemical reaction with just two species. This is a model showing oscillatory behavior MacOS: Adjust "System Preferences" -> "Security & Privacy" to allow Java JSim jnlp app to execute.įigure 1: The phase plane plots showing oscillatory behavior. (JSim model may take 10-20 seconds to load.) Increases from 0.25 to 0.95, the model switches from a stable equilibrium point to a limit cycle nearī=0.41 and back to a stable equilibrium point near b=0.8. The Selkov model for glycolysis exhibits a Hopf bifurcation.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |