Optimizing charge-balanced pulse stimulation for desynchronization
- Collective synchronization in a large population of self-sustained units appears both in natural and engineered systems. Sometimes this effect is in demand, while in some cases, it is undesirable, which calls for control techniques. In this paper, we focus on pulsatile control, with the goal to either increase or decrease the level of synchrony. We quantify this level by the entropy of the phase distribution. Motivated by possible applications in neuroscience, we consider pulses of a realistic shape. Exploiting the noisy Kuramoto-Winfree model, we search for the optimal pulse profile and the optimal stimulation phase. For this purpose, we derive an expression for the change of the phase distribution entropy due to the stimulus. We relate this change to the properties of individual units characterized by generally different natural frequencies and phase response curves and the population's state. We verify the general result by analyzing a two-frequency population model and demonstrating a good agreement of the theory and numericalCollective synchronization in a large population of self-sustained units appears both in natural and engineered systems. Sometimes this effect is in demand, while in some cases, it is undesirable, which calls for control techniques. In this paper, we focus on pulsatile control, with the goal to either increase or decrease the level of synchrony. We quantify this level by the entropy of the phase distribution. Motivated by possible applications in neuroscience, we consider pulses of a realistic shape. Exploiting the noisy Kuramoto-Winfree model, we search for the optimal pulse profile and the optimal stimulation phase. For this purpose, we derive an expression for the change of the phase distribution entropy due to the stimulus. We relate this change to the properties of individual units characterized by generally different natural frequencies and phase response curves and the population's state. We verify the general result by analyzing a two-frequency population model and demonstrating a good agreement of the theory and numerical simulations.…
| Author details: | Erik Thomas Klaus MauORCiD, Michael RosenblumORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1063/5.0070036 |
| ISSN: | 1054-1500 |
| ISSN: | 1089-7682 |
| Pubmed ID: | https://pubmed.ncbi.nlm.nih.gov/35105136 |
| Title of parent work (English): | Chaos : an interdisciplinary journal of nonlinear science |
| Publisher: | AIP |
| Place of publishing: | Melville |
| Publication type: | Article |
| Language: | English |
| Date of first publication: | 2022/01/03 |
| Publication year: | 2022 |
| Release date: | 2023/04/21 |
| Volume: | 32 |
| Issue: | 1 |
| Article number: | 013103 |
| Number of pages: | 15 |
| Funding institution: | Deutsche Forschungsgemeinschaft (DFG, German Research Foundation); [424778381-TRR 295] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
| DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |
| Peer review: | Referiert |
