×

zbMATH — the first resource for mathematics

Periodic solutions and bifurcations of delay-differential equations. (English) Zbl 1195.34116
Summary: A simple but effective iteration method is proposed to search for limit cycles or bifurcation curves of delay-differential equations. An example is given to illustrate its convenience and effectiveness.

MSC:
34K23 Complex (chaotic) behavior of solutions to functional-differential equations
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34K18 Bifurcation theory of functional-differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Peng, M.; Ucar, A., Chaos solitons fractals, 21, 883, (2004)
[2] He, J.-H., Int. J. non-linear mech., 35, 37, (2000)
[3] He, J.-H., Int. J. non-linear sci. numer. simul., 6, 2, 207, (2005)
[4] El-Shahed, M., Int. J. non-linear sci. numer. simul., 6, 2, 163, (2005)
[5] He, J.-H., Int. J. non-linear mech., 34, 4, 699, (1999)
[6] Drăgănescu, Gh.-E.; Căpălnăşan, V., Int. J. non-linear sci. numer. simul., 4, 3, 219, (2004)
[7] He, J.-H., Int. J. non-linear mech., 37, 2, 309, (2002)
[8] He, J.-H., Int. J. non-linear mech., 37, 2, 315, (2002)
[9] Liu, H.M., Chaos solitons fractals, 23, 577, (2005)
[10] Liu, H.M., Int. J. non-linear sci. numer. simul., 5, 1, 95, (2004)
[11] He, J.-H., Chaos soliton fractals, 19, 4, 847, (2004)
[12] Hao, T.H., Int. J. non-linear sci. numer. simul., 4, 3, 307, (2003)
[13] Hao, T.H., Int. J. non-linear sci. numer. simul., 4, 3, 311, (2003)
[14] Hao, T.H., Int. J. non-linear sci. numer. simul., 6, 2, 209, (2005)
[15] He, J.-H., Int. J. non-linear sci. numer. simul., 4, 3, 313, (2003)
[16] Zayed, E.M.E.; Zedan, H.A.; Gepreel, K.A., Int. J. non-linear sci. numer. simul., 5, 3, 221, (2004)
[17] Abdusalam, H.A., Int. J. non-linear sci. numer. simul., 6, 2, 99, (2005)
[18] Abassy, T.A.; El-Tawil, M.A.; Saleh, H.K., Int. J. non-linear sci. numer. simul., 5, 4, 327, (2004)
[19] Shen, J.; Xu, W., Int. J. non-linear sci. numer. simul., 5, 4, 397, (2004)
[20] Ma, S.; Lu, Q., Int. J. non-linear sci. numer. simul., 6, 1, 13, (2005)
[21] Zhang, Y.; Xu, J., Int. J. non-linear sci. numer. simul., 6, 1, 63, (2005)
[22] Zhang, Z.; Bi, Q., Int. J. non-linear sci. numer. simul., 6, 1, 81, (2005)
[23] Zheng, Y.; Fu, Y., Int. J. non-linear sci. numer. simul., 6, 1, 87, (2005)
[24] Nada, S.I., Int. J. non-linear sci. numer. simul., 6, 2, 145, (2005)
[25] Ucar, A.; Bishop, S.R., Int. J. non-linear sci. numer. simul., 2, 3, 289, (2001)
[26] He, J.-H., Phys. rev. lett., 90, 17, 174301, (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.