3 research outputs found
Network-Induced Oscillatory Behavior in Material Flow Networks
Network theory is rapidly changing our understanding of complex systems, but
the relevance of topological features for the dynamic behavior of metabolic
networks, food webs, production systems, information networks, or cascade
failures of power grids remains to be explored. Based on a simple model of
supply networks, we offer an interpretation of instabilities and oscillations
observed in biological, ecological, economic, and engineering systems. We find
that most supply networks display damped oscillations, even when their units -
and linear chains of these units - behave in a non-oscillatory way. Moreover,
networks of damped oscillators tend to produce growing oscillations. This
surprising behavior offers, for example, a new interpretation of business
cycles and of oscillating or pulsating processes. The network structure of
material flows itself turns out to be a source of instability, and cyclical
variations are an inherent feature of decentralized adjustments.Comment: For related work see http://www.helbing.or
On Stability Problems of Supply Networks Constrained With Transport Delay
International audienceTransportation is one of the most crucial components in supply networks. In transportation lines, there exists a finite time between products leaving a point and arriving to another point in the supply network. This period of time is the delay, which accompanies all transportation lines present in the entire network. Delay is a well-known limitation, which is inevitable and pervasive in the network causing synchronization problems, fluctuating or excessive inventories, and lack of robustness of inventories against cyclic perturbations. The end results of such undesirable effects directly reflect to costs. This paper is motivated to reveal the mechanisms leading to these problems by analytically characterizing qualitative behavior of supply network dynamics modeled by continuous-time differential equations. The presence of delay forms the main challenge in the analysis and this is tackled by developing/utilizing the tools emerging from delay systems and control theory. While the backbone of the paper addresses the qualitative behavior in presence of a single delay representing delays in all transportation paths, it also reveals how to choose production rates and transportation delay without inducing any undesirable effects mentioned. Thorough cases studies with single and multiple delays are presented to demonstrate the effectiveness of the approaches proposed