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Stabilization of causally and non-causally coupled map lattices

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  • Atmanspacher, Harald
  • Scheingraber, Herbert

Abstract

Two-dimensional coupled map lattices have global stability properties that depend on the coupling between individual maps and their neighborhood. The action of the neighborhood on individual maps can be implemented in terms of “causal” coupling (to spatially distant past states) or “non-causal” coupling (to spatially distant simultaneous states). In this contribution we show that globally stable behavior of coupled map lattices is facilitated by causal coupling, thus indicating a surprising relationship between stability and causality. The influence of causal versus non-causal coupling for synchronous and asynchronous updating as a function of coupling strength and for different neighborhoods is analyzed in detail.

Suggested Citation

  • Atmanspacher, Harald & Scheingraber, Herbert, 2005. "Stabilization of causally and non-causally coupled map lattices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 345(3), pages 435-447.
    • Handle: RePEc:eee:phsmap:v:345:y:2005:i:3:p:435-447
    DOI: 10.1016/j.physa.2004.07.020
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    References listed on IDEAS

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    1. Masoller, Cristina & Martı́, Arturo C & Zanette, Damián H, 2003. "Synchronization in an array of globally coupled maps with delayed interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(1), pages 186-191.
    2. Gelover-Santiago, A.L & Lima, R & Martı́nez-Mekler, G, 2000. "Synchronization and cluster periodic solutions in globally coupled maps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(1), pages 131-135.
    3. Li, Chunguang & Li, Shaowen & Liao, Xiaofeng & Yu, Juebang, 2004. "Synchronization in coupled map lattices with small-world delayed interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 365-370.
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    Cited by:

    1. Karataieva, Tatiana & Koshmanenko, Volodymyr & Krawczyk, Małgorzata J. & Kułakowski, Krzysztof, 2019. "Mean field model of a game for power," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 535-547.
    2. Dobyns, York & Atmanspacher, Harald, 2006. "Information flow between weakly interacting lattices of coupled maps," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 755-767.

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