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Revealing instabilities in a generalized triadic supply network: a bifurcation analysis

Ritterskamp, Daniel and Demirel, Guven and MacCarthy, Bart L and Rudolf, Lars and Champneys, Alan R and Gross, Thilo (2018) 'Revealing instabilities in a generalized triadic supply network: a bifurcation analysis.' Chaos, 28 (7). 073103-073103. ISSN 1054-1500

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Supply networks are exposed to instabilities and thus a high level of risk. To mitigate this risk, it is necessary to understand how instabilities are formed in supply networks. In this paper, we focus on instabilities in inventory dynamics that develop due to the topology of the supply network. To be able to capture these topology-induced instabilities, we use a method called generalized modeling, a minimally specified modeling approach adopted from ecology. This method maps the functional dependencies of production rates on the inventory levels of different parts and products, which are imposed by the network topology, to a set of elasticity parameters. We perform a bifurcation analysis to investigate how these elasticities affect the stability. First, we show that dyads and serial supply chains are immune to topology-induced instabilities. In contrast, in a simple triadic network, where a supplier acts as both a first and a second tier supplier, we can identify instabilities that emerge from saddle-node, Hopf, and global homoclinic bifurcations. These bifurcations lead to different types of dynamical behavior, including exponential convergence to and divergence from a steady state, temporary oscillations around a steady state, and co-existence of different types of dynamics, depending on initial conditions. Finally, we discuss managerial implications of the results.

Item Type: Article
Uncontrolled Keywords: supply network, stability, generalized modeling, nonlinear dynamics, bifurcation, triadic interactions
Subjects: H Social Sciences > HD Industries. Land use. Labor
Q Science > QA Mathematics
Divisions: Faculty of Social Sciences
Faculty of Social Sciences > Essex Business School
Faculty of Social Sciences > Essex Business School > Management Science and Entrepreneurship Group
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 09 Aug 2018 10:00
Last Modified: 06 Jan 2022 13:51

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