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Symmetry breaking, bifurcations, periodicity and chaos in the Euler method for a class of delay differential equations

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  • Peng, Mingshu

Abstract

A discrete model is proposed to explore the rich dynamics of nonlinear delayed systems under Euler discretization, such as multiple steady states, multiple bifurcations, complex periodic oscillations, and chaos.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:5:p:1287-1297
    DOI: 10.1016/j.chaos.2004.09.049
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    Cited by:

    1. Peng, Mingshu & Yuan, Yuan, 2008. "Complex dynamics in discrete delayed models with D4 symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 393-408.
    2. Attili, Basem S., 2009. "A direct method for the numerical computation of bifurcation points underlying symmetries," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1545-1551.
    3. Morel, C. & Vlad, R. & Morel, J.-Y. & Petreus, D., 2011. "Generating chaotic attractors on a surface," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(11), pages 2549-2563.

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