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Abstract

Due to characteristics such as fluctuations with bursts, intermittence and heavy-tailed distributions, Lévy noise can provide reliable convenience for simulating the bursty random factors experienced by epilepsy patients. However, the existing studies are mostly limited to Gaussian white noise and harmonic excitation, which inspired us to try to combine Lévy noise with epilepsy model. Our results show that a transition behavior between the healthy alpha rhythm and epileptiform waveform in the bistable parameter region can be induced by Lévy noise. In fact, it is caused by the large jumps of the Lévy noise appearing in the right positions and with adequate intensity. With the help of Monte Carlo simulation, the intensity and stability index of Lévy noise are proven to effectively influence the transition dynamics, while the skewness parameter does not. For comparison, Gaussian white noise and single-pulse stimulation are also considered. We conclude that the former cannot induce such a transition behavior, while the latter can achieve a similar effect to Lévy noise, except that the required stimulus intensity is larger. In addition, we also provide the intrinsic mechanisms for the initiation and termination of epilepsy from the perspective of attractive basins, and find that it is closely related to the geometry of the basin of attraction. These results should shed light on studies of epilepsy and neurological diseases, as well as the development of neuromodulation strategies.