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An algorithm for engineering regime shifts in one-dimensional dynamical systems

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  • Tan, James P.L.

Abstract

Regime shifts are discontinuous transitions between stable attractors hosting a system. They can occur as a result of a loss of stability in an attractor as a bifurcation is approached. In this work, we consider one-dimensional dynamical systems where attractors are stable equilibrium points. Relying on critical slowing down signals related to the stability of an equilibrium point, we present an algorithm for engineering regime shifts such that a system may escape an undesirable attractor into a desirable one. We test the algorithm on synthetic data from a one-dimensional dynamical system with a multitude of stable equilibrium points and also on a model of the population dynamics of spruce budworms in a forest. The algorithm and other ideas discussed here contribute to an important part of the literature on exercising greater control over the sometimes unpredictable nature of nonlinear systems.

Suggested Citation

  • Tan, James P.L., 2018. "An algorithm for engineering regime shifts in one-dimensional dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 721-731.
    • Handle: RePEc:eee:phsmap:v:490:y:2018:i:c:p:721-731
    DOI: 10.1016/j.physa.2017.08.140
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    References listed on IDEAS

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    1. James Tan & Siew Cheong, 2014. "Critical slowing down associated with regime shifts in the US housing market," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(2), pages 1-10, February.
    2. James Tan & Siew Ann Cheong, 2016. "The Regime Shift Associated with the 2004–2008 US Housing Market Bubble," PLOS ONE, Public Library of Science, vol. 11(9), pages 1-8, September.
    3. Marten Scheffer & Jordi Bascompte & William A. Brock & Victor Brovkin & Stephen R. Carpenter & Vasilis Dakos & Hermann Held & Egbert H. van Nes & Max Rietkerk & George Sugihara, 2009. "Early-warning signals for critical transitions," Nature, Nature, vol. 461(7260), pages 53-59, September.
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