https://doi.org/10.1140/epjs/s11734-025-01658-0
Regular Article
Perturbation-driven of stability and phase transition in balanced rate-based networks
1
School of Physics and Electronic Engineering, Jiangsu University, Xuefu Road 301, 212013, Zhenjiang, Jiangsu, China
2
Teaching Department, Jiangsu University Jingjiang College, Changxiangxi Road 537, 212028, Zhenjiang, Jiangsu, China
3
School of Mathematical Sciences, Jiangsu University, Xuefu Road 301, 212013, Zhenjiang, Jiangsu, China
Received:
4
March
2025
Accepted:
24
April
2025
Published online:
25
May
2025
The stability of neural networks has primarily been studied through the lenses of synaptic weights and external perturbations in the context of computational cognition in the brain. However, it remains unclear how balanced neural networks respond to different external inputs, which continues to be an elusive question. We present a rate-based excitatory-inhibitory (EI) network to explore dynamic stability and the transition boundaries between various fixed points. In scenarios with weaker excitatory coupling, we find that rate-based neural networks not only exhibit stable nodes but also contain regions devoid of equilibrium points with various parameters of external perturbations. These findings suggest that this balanced network can maintain robust dynamical behavior to different types of external perturbation. With stronger excitatory coupling, the rate-based network can display three distinct types of dynamical states: unstable saddles, the coexistence of stable nodes alongside unstable saddles, and a complete absence of equilibrium points under different combinations of external perturbations. These dynamic regimes, arising from stronger excitatory coupling, are sensitive to external perturbations due to unstable saddles. Furthermore, the dynamical boundaries and eigenvalues observed in our numerical results are strongly supported by robust theoretical evidence, reinforcing the validity of our conclusions.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
