Modulating bifurcations in a self-sustained birhythmic system by α-stable Levy noise and time delay

Birhythmical nature has been widely encountered and has aroused considerable interest in controlling dynamic behaviors of a self-sustained birhythmic system. However, researchers focus a lot on bifurcations induced by idealized Gaussian noises, the Gaussianity of which can be violated in natural phenomena. The birhythmic oscillator is well suited for modeling biological systems, especially for simulating enzymatic reactions. There are many relevant articles, but few examine the effects of non-Gaussian noises on dynamics of birhythmic systems. -stable Levy noise is more appropriate to characterize complicated biological surroundings. Besides, a few investigations simultaneously introduce the Levy noise and the inevitable time delay. Control of bifurcations in a birhythmic system driven by alpha-stable Levy noise and time delay is numerically studied in this work, with three noise and two delay parameters treated as control parameters. Modulating the stability index and noise intensity can govern dynamics of the system, but regulating the skewness parameter cannot. More abundant bifurcations are available from adjusting the strength of delayed feedback and time delay. These results may be conducive to further exploring bifurcations in the real-world applications.