Amplitude-modulated bursting (AMB), characterized by oscillations appearing in the envelope of the active phase of bursting, is a novel class of bursting rhythms reported recently. The present paper aims to report a simple and effective method, i.e., the multiple-frequency slow parametric modulation (MFSPM) method, for obtaining such a bursting pattern. We show that the MFSPM can be well controlled so that it may exhibit multiple continuous ups and downs in the active area. Then, the amplitude of the traced active state alternates between increases and decreases accordingly, which leads to oscillations in the envelope of the active phase, and AMB is thus created. Based on this, the route to AMB by the MFSPM is presented. The validity of the approach is demonstrated by several examples. The proposed approach does not depend on specific systems or bifurcations and thus is a general method.

• Received 29 October 2017

DOI:https://doi.org/10.1103/PhysRevE.97.012202