Detection of bistable structures via the Conley index and applications to biological systems
Dynamical Systems
2021-03-09 v1
Abstract
Bistability is a ubiquitous phenomenon in life sciences. In this paper, two kinds of bistable structures in dynamical systems are studied: One is two one-point attractors, another is a one-point attractor accompanied by a cycle attractor. By the Conley index theory, we prove that there exist other isolated invariant sets besides the two attractors, and also obtain the possible components and their configuration. Moreover, we find that there is always a separatrix or cycle separatrix, which separates the two attractors. Finally, the biological meanings and implications of these structures are given and discussed.
Keywords
Cite
@article{arxiv.2103.04361,
title = {Detection of bistable structures via the Conley index and applications to biological systems},
author = {Junbo Jia and Pan Yang and Huaiping Zhu and Zhen Jin and Jinqiao Duan and Xinchu Fu},
journal= {arXiv preprint arXiv:2103.04361},
year = {2021}
}
Comments
23 pages, 13 figures