Detection of bistable structures via the Conley index and applications to biological systems

2021/03/07 by Junbo Jia, Yang Pan, Jia, Junbo +9
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · #34D45 #37B30 #92B05 #Dynamical Systems (math.DS) #FOS: Mathematics #Gene Regulatory Network Analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.2103.04361

openalex publication_date 2021/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A generalization of the Kermack-McKendrick deterministic epidemic model
• Backward bifurcation of an epidemic model with treatment

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