作者
Katherine Morrison, Anda Degeratu, Vladimir Itskov, Carina Curto
发表日期
2024/3/31
期刊
SIAM Journal on Applied Dynamical Systems
卷号
23
期号
1
页码范围
855-884
出版商
Society for Industrial and Applied Mathematics
简介
Threshold-linear networks consist of simple units interacting in the presence of a threshold nonlinearity. Competitive threshold-linear networks have long been known to exhibit multistability, where the activity of the network settles into one of potentially many steady states. In this work, we find conditions that guarantee the absence of steady states, while maintaining bounded activity. These conditions lead us to define a combinatorial family of competitive threshold-linear networks, parametrized by a simple directed graph. By exploring this family, we discover that threshold-linear networks are capable of displaying a surprisingly rich variety of nonlinear dynamics, including limit cycles, quasi-periodic attractors, and chaos. In particular, several types of nonlinear behaviors can co-exist in the same network. Our mathematical results also enable us to engineer networks with multiple dynamic patterns. Taken together …
学术搜索中的文章
K Morrison, A Degeratu, V Itskov, C Curto - arXiv preprint arXiv:1605.04463, 2016
K Morrison, A Degeratu, V Itskov, C Curto - SIAM Journal on Applied Dynamical Systems, 2024