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Effective approaches to explore rich dynamics of delay-differential equations

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  • Peng, Mingshu

Abstract

Discrete models are proposed to delve into the rich dynamics of nonlinear delayed systems under Euler discretization, such as backwards bifurcations, stable limit cycles, multiple limit-cycle bifurcations and chaotic behavior. The effect of breaking the special symmetry of the system is to create a wide complex operating conditions which would not otherwise be seen. These include multiple steady states, complex periodic oscillations, chaos by period doubling bifurcations. Effective computation of multiple bifurcations, stable limit cycles, symmetrical breaking bifurcations and chaotic behavior in nonlinear delayed equations is developed.

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  • Peng, Mingshu, 2005. "Effective approaches to explore rich dynamics of delay-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1131-1140.
    • Handle: RePEc:eee:chsofr:v:25:y:2005:i:5:p:1131-1140
    DOI: 10.1016/j.chaos.2004.11.086
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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.

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