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Complex dynamics in discrete delayed models with D4 symmetry

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  • Peng, Mingshu
  • Yuan, Yuan

Abstract

In this paper, we consider nonlinear time-delayed models with four identical resonators. Detailed analysis about equivariant bifurcations coupled with the Lie group actions on vector spaces is offered, including equivariant Neimark–Sacker bifurcations, equivariant pitchfork bifurcations and equivariant periodic doubling bifurcations. Pattern formation, spatio-temporal behavior and mode interactions are shown in a discrete nonlinear optical model involving a time-delayed feedback.

Suggested Citation

  • Peng, Mingshu & Yuan, Yuan, 2008. "Complex dynamics in discrete delayed models with D4 symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 393-408.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:2:p:393-408
    DOI: 10.1016/j.chaos.2006.08.048
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    References listed on IDEAS

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    1. Peng, Mingshu, 2005. "Effective approaches to explore rich dynamics of delay-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1131-1140.
    2. Peng, Mingshu, 2005. "Symmetry breaking, bifurcations, periodicity and chaos in the Euler method for a class of delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1287-1297.
    3. Peng, Mingshu, 2005. "Rich dynamics of discrete delay ecological models," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1279-1285.
    4. Peng, Mingshu, 2005. "Multiple bifurcations and periodic “bubbling” in a delay population model," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1123-1130.
    5. Masoller, Cristina & Zanette, nindexDamianDamia’an H., 2001. "Anticipated synchronization in coupled chaotic maps with delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(3), pages 359-366.
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    Cited by:

    1. Zhang, Chunrui & Zheng, Baodong, 2009. "Bifurcation in Z2-symmetry quadratic polynomial systems with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3078-3086.

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