Abstract
The dynamics of an oscillator, which exhibits a stable equilibrium and a stable limit cycle, is investigated. We refer to it as a bistable oscillator unit (BOU) and show that two coupled BOUs (CBOUs) exhibit dynamics analogous to neural activity patterns in epilepsy, including healthy, localized, and fully spread epileptic states. By treating each CBOU as an independent system influenced by the state of the other, we establish local input-to-state stability near the equilibrium and the limit cycle and estimate the ultimate bounds of the trajectories. Our analysis identifies the domain of the initial conditions and estimates the coupling parameter critical in determining the epileptic behavior of the CBOUs. The actual value of the coupling parameter, above which the dynamics transition from localized to fully spread epileptic states, is determined through simulations; the results closely match the derived analytical estimate.
Recommended Citation
N. Kant and R. Mukherjee, "Investigating Bistable Dynamics of Coupled Oscillators with Similarities to Neural Activity in Epilepsy," IEEE Control Systems Letters, vol. 8, pp. 2919 - 2924, Institute of Electrical and Electronics Engineers, Jan 2024.
The definitive version is available at https://doi.org/10.1109/LCSYS.2024.3519014
Department(s)
Mechanical and Aerospace Engineering
Keywords and Phrases
Bistability; coupled oscillator; epilepsy; input-to-state stability; limit cycle; modeling; nonlinear dynamics; seizures
International Standard Serial Number (ISSN)
2475-1456
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2025 Institute of Electrical and Electronics Engineers, All rights reserved.
Publication Date
01 Jan 2024
