title: Global stability analysis of birhythmicity in a self-sustained oscillator.
abstract: We analyze the global stability properties of birhythmicity in a self-sustained system with random excitations. The model is a multi-limit-cycle variation in the van der Pol oscillator introduced to analyze enzymatic substrate reactions in brain waves. We show that the two frequencies are strongly influenced by the nonlinear coefficients alpha and beta. With a random excitation, such as a Gaussian white noise, the attractor's global stability is measured by the mean escape time tau from one limit cycle. An effective activation energy barrier is obtained by the slope of the linear part of the variation in the escape time tau versus the inverse noise intensity 1/D. We find that the trapping barriers of the two frequencies can be very different, thus leaving the system on the same attractor for an overwhelming time. However, we also find that the system is nearly symmetric in a narrow range of the parameters.
authors.affiliation: Department of Physics, Group of Nonlinear Physics and Complex System, Faculty of Science, Fundamental Physics Laboratory, University of Douala, Box 24157, Douala, Cameroon. ryamapi@yahoo.fr
authors.forename: R
authors.initials: R
authors.lastname: Yamapi
authors.forename: G
authors.initials: G
authors.lastname: Filatrella
authors.forename: M A
authors.initials: MA
authors.lastname: Aziz-Alaoui
mesh_terms: D000465:Algorithms; D000818:Animals; D001703:Biophysics / Q000379:methods*; D002940:Circadian Rhythm; D006801:Humans; D007700:Kinetics; D008959:Models, Neurological; D015233:Models, Statistical; D008962:Models, Theoretical; D009415:Nerve Net; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D009991:Oscillometry / Q000379:methods; D011506:Proteins / Q000737:chemistry*
chemical_list: D011506:Proteins