Sequential chaotic oscillations in excitatory-inhibitory threshold-linear networks
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914619609579520 |
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| author | Zang, Jie Curto, Carina |
| author_facet | Zang, Jie Curto, Carina |
| contents | Metastable states, a phenomenon observed in brain dynamics and many other systems, have been proposed as a key feature of healthy brain function, reflecting a balance between integration and segregation. However, it remains unclear how to capture this behavior within a dynamical-systems framework. In this paper, we propose sequential chaotic oscillations (SCOs), arising in excitatory-inhibitory threshold-linear networks (E-I TLNs), as a candidate dynamical mechanism for sequential metastability. As a simple form of chaotic itinerancy, SCOs occur under constant input and consist of a sequence of metastable states whose transition order can be predicted by the underlying graph. To identify the parameter regime for SCOs, we develop new graph rules for E-I TLNs and use them to characterize the fixed point structure of E-I TLNs on paths and cycles. Our results show that the emergence of SCOs requires unstable singleton fixed points and sufficiently strong inhibition. In addition to SCOs, we find that E-I oscillations need not be synchronized. Motivated by this, we introduce a decomposition into the z-mode and the mean mode, which capture excitatory differences and overall network activity, respectively. These modes are then used to distinguish attractors associated with the full-support fixed point of E-I TLNs on cycles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00373 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sequential chaotic oscillations in excitatory-inhibitory threshold-linear networks Zang, Jie Curto, Carina Neurons and Cognition Metastable states, a phenomenon observed in brain dynamics and many other systems, have been proposed as a key feature of healthy brain function, reflecting a balance between integration and segregation. However, it remains unclear how to capture this behavior within a dynamical-systems framework. In this paper, we propose sequential chaotic oscillations (SCOs), arising in excitatory-inhibitory threshold-linear networks (E-I TLNs), as a candidate dynamical mechanism for sequential metastability. As a simple form of chaotic itinerancy, SCOs occur under constant input and consist of a sequence of metastable states whose transition order can be predicted by the underlying graph. To identify the parameter regime for SCOs, we develop new graph rules for E-I TLNs and use them to characterize the fixed point structure of E-I TLNs on paths and cycles. Our results show that the emergence of SCOs requires unstable singleton fixed points and sufficiently strong inhibition. In addition to SCOs, we find that E-I oscillations need not be synchronized. Motivated by this, we introduce a decomposition into the z-mode and the mean mode, which capture excitatory differences and overall network activity, respectively. These modes are then used to distinguish attractors associated with the full-support fixed point of E-I TLNs on cycles. |
| title | Sequential chaotic oscillations in excitatory-inhibitory threshold-linear networks |
| topic | Neurons and Cognition |
| url | https://arxiv.org/abs/2606.00373 |