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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Stability and Bifurcation Analysis in a Two-Dimensional Neutral Differential Equation

Discontinuity, Nonlinearity, and Complexity 8(4) (2019) 391--402 | DOI:10.5890/DNC.2019.12.004

A. Moussaid, Talibi Alaoui Hamad

Department of Mathematics, Faculty of Science, University Chouaib Doukkali BP. 20, 24000, El Jadida Morocco

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This paper discusses asymptotic stability and Hopf bifurcations occurs at the origin in certain two-dimensional neutral delay differential equations. We give necessary and sufficient conditions on the parameters to obtain the asymptotic stability and bifurcations. Global existence of periodic solutions is established using a global Hopf bifurcation result of Krawcewicz et al. Finally, some numerical simulations are carried out to support the analytic results. Our results are a generalization of M. Liu and X. Xu [1].


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