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Stability and Bifurcations of Equilibria in Networks with Piecewise Linear Interactions.
- Source :
-
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering . 2021, Vol. 31 Issue 11, p1-27. 27p. - Publication Year :
- 2021
-
Abstract
- In this paper, we study equilibria of differential equation models for networks. When interactions between nodes are taken to be piecewise constant, an efficient combinatorial analysis can be used to characterize the equilibria. When the piecewise constant functions are replaced with piecewise linear functions, the equilibria are preserved as long as the piecewise linear functions are sufficiently steep. Therefore the combinatorial analysis can be leveraged to understand a broader class of interactions. To better understand how broad this class is, we explicitly characterize how steep the piecewise linear functions must be for the correspondence between equilibria to hold. To do so, we analyze the steady state and Hopf bifurcations which cause a change in the number or stability of equilibria as slopes are decreased. Additionally, we show how to choose a subset of parameters so that the correspondence between equilibria holds for the smallest possible slopes when the remaining parameters are fixed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02181274
- Volume :
- 31
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 152206535
- Full Text :
- https://doi.org/10.1142/S0218127421300329