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Abstract High frequency excitation (HFE) is known to induce various nontrivial effects, such as system stiffening, biasing, and the smoothing of discontinuities in dynamical systems. These effects become increasingly pertinent in multi-stable systems, where the system’s bias towards a certain equilibrium state can depend heavily on the combination of forcing parameters, leading to stability in some scenarios and instability in others. In this initial investigation, our objective is to pinpoint the specific parameter ranges in which the bistable system demonstrates typical HFE effects, both through numerical simulations and experimental observations. To accomplish this, we utilize the method of multiple scales to analyze the interplay among different time scales. The equation of slow dynamics reveals how the excitation parameters lead to a change in stability of equilibrium points. Additionally, we delineate the parameter ranges where stabilizing previously unstable equilibrium configurations is achievable. We demonstrate the typical positional biasing effect of high-frequency excitation that leads to a shift in the equilibrium points as the excitation parameter is varied. This kind of excitation can enable the active shaping of potential wells. Finally, we qualitatively validate our numerical findings through experimental testing using a simplistic model made with LEGOs.
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Stabilization of Weakly Unstable Fixed Points as a Common Dynamical Mechanism of High-Frequency Electrical Stimulation
Abstract While high-frequency electrical stimulation often used to treat various biological diseases, it is generally difficult to understand its dynamical mechanisms of action. In this work, high-frequency electrical stimulation is considered in the context of neurological and cardiological systems. Despite inherent differences between these systems, results from both theory and computational modeling suggest identical dynamical mechanisms responsible for desirable qualitative changes in behavior in response to high-frequency stimuli. Specifically, desynchronization observed in a population of periodically firing neurons and reversible conduction block that occurs in cardiomyocytes both result from bifurcations engendered by stimulation that modifies the stability of unstable fixed points. Using a reduced order phase-amplitude modeling framework, this phenomenon is described in detail from a theoretical perspective. Results are consistent with and provide additional insight for previously published experimental observations. Also, it is found that sinusoidal input is energy-optimal for modifying the stability of weakly unstable fixed points using periodic stimulation.
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- Award ID(s):
- 1933583
- PAR ID:
- 10154438
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Scientific Reports
- Volume:
- 10
- Issue:
- 1
- ISSN:
- 2045-2322
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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