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Dynamics and equilibria of ecological predator–prey networks as nature’s supply chains

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  • Nagurney, Anna
  • Nagurney, Ladimer S.

Abstract

In this paper, we develop a dynamic network model of ecological food webs and prove that the set of stationary points of the projected dynamical system coincides with the set of solutions of a variational inequality governing the equilibrium of predator–prey networks. We also establish the equivalence between the ecological models and supply chain network equilibrium models and highlight the connections to spatial price equilibrium problems. We propose an algorithmic scheme, provide convergence results, and apply it to a food web drawn from a fisheries application.

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  • Nagurney, Anna & Nagurney, Ladimer S., 2012. "Dynamics and equilibria of ecological predator–prey networks as nature’s supply chains," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 89-99.
    • Handle: RePEc:eee:transe:v:48:y:2012:i:1:p:89-99
    DOI: 10.1016/j.tre.2011.07.007
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    References listed on IDEAS

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    1. Florian, Michael & Los, Marc, 1982. "A new look at static spatial price equilibrium models," Regional Science and Urban Economics, Elsevier, vol. 12(4), pages 579-597, November.
    2. Cruz, Jose M. & Wakolbinger, Tina, 2008. "Multiperiod effects of corporate social responsibility on supply chain networks, transaction costs, emissions, and risk," International Journal of Production Economics, Elsevier, vol. 116(1), pages 61-74, November.
    3. Nagurney, Anna & Dong, June & Zhang, Ding, 2002. "A supply chain network equilibrium model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 38(5), pages 281-303, September.
    4. Nagurney, Anna & Liu, Zugang & Cojocaru, Monica-Gabriela & Daniele, Patrizia, 2007. "Dynamic electric power supply chains and transportation networks: An evolutionary variational inequality formulation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(5), pages 624-646, September.
    5. Walter C. Labys & Chin W. Yang, 1997. "Spatial Price Equilibrium As A Foundation To Unified Spatial Commodity Modeling," Papers in Regional Science, Wiley Blackwell, vol. 76(2), pages 199-228, April.
    6. Zugang Liu & Anna Nagurney, 2007. "Financial Networks with Intermediation and Transportation Network Equilibria: A Supernetwork Equivalence and Reinterpretation of the Equilibrium Conditions with Computations," Computational Management Science, Springer, vol. 4(3), pages 243-281, July.
    7. Daniele, Patrizia, 2010. "Evolutionary variational inequalities and applications to complex dynamic multi-level models," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(6), pages 855-880, November.
    8. Mullon, Christian & Shin, Yunne & Cury, Philippe, 2009. "NEATS: A Network Economics Approach to Trophic Systems," Ecological Modelling, Elsevier, vol. 220(21), pages 3033-3045.
    9. Anna Nagurney, 2006. "Supply Chain Network Economics," Books, Edward Elgar Publishing, number 4242.
    10. Zhang, Ding, 2006. "A network economic model for supply chain versus supply chain competition," Omega, Elsevier, vol. 34(3), pages 283-295, June.
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    Cited by:

    1. Waters, Edward K. & Sidhu, Harvinder S. & Sidhu, Leesa A. & Mercer, Geoffry N., 2015. "Extended Lotka–Volterra equations incorporating population heterogeneity: Derivation and analysis of the predator–prey case," Ecological Modelling, Elsevier, vol. 297(C), pages 187-195.

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