Regular Article

Lévy noise induced transitions and enhanced stability in a birhythmic van der Pol system

¹ Fundamental Physics Laboratory, Physics of Complex System Group, Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon
² Potsdam Institute for Climate Impact Research (PIK), 14473 Potsdam, Germany
³ Laboratory of Mechanics and Materials, Department of Physics, Faculty of Science, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon
⁴ Department of Sciences and Technologies and Salerno unit of CNSIM, University of Sannio, Via Port’Arsa 11, 82100 Benevento, Italy
⁵ Department of Physics, Humboldt University, 12489 Berlin, Germany

^a e-mail: ryamapi@yahoo.fr

Received: 22 January 2019
Received in final form: 29 April 2019
Published online: 10 July 2019

Abstract

This work describes the effects of Lévy noise on a birhythmic van der Pol like oscillator. The two periodic attractors are characterized by different periods, and the stability in the presence of Gaussian noise can be described by an effective, or quasi-potential. Numerical simulations demonstrate that in the presence of Lévy noise the induced escapes from an attractor to another are similar to the escapes between stable points in an ordinary potential. Assuming that the attractors are almost separated by a barrier of a quasi (or pseudo) potential, the theory for Lévy noise escapes captures the qualitative features of the escapes across the quasi-potential. The differences to the Gaussian case are more pronounced for large values of the Lévy index. We found that for the symmetric quasi-potential, the relative stability of the two attractors are similar, while in the asymmetric case the properties of the two attractors differ for increasing a. The global stability is also characterized by means of the residence times, that give indications for future theoretical analysis.