Jiang, Minghui; Shen, Yi; Jian, Jigui; Liao, Xiaoxin Stability, bifurcation and a new chaos in the logistic differential equation with delay. (English) Zbl 1195.34117 Phys. Lett., A 350, No. 3-4, 221-227 (2006). Summary: This Letter is concerned with bifurcation and chaos in the logistic delay differential equation with a parameter \(r\). The linear stability of the logistic equation is investigated by analyzing the associated characteristic transcendental equation. Based on the normal form approach and the center manifold theory, the formula for determining the direction of Hopf bifurcation and the stability of bifurcation periodic solution in the first bifurcation values is obtained. By theoretical analysis and numerical simulation, we found a new chaos in the logistic delay differential equation. Cited in 14 Documents MSC: 34K23 Complex (chaotic) behavior of solutions to functional-differential equations 34K18 Bifurcation theory of functional-differential equations 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior Keywords:logistic delay differential equation; stability; bifurcation; chaos PDF BibTeX XML Cite \textit{M. Jiang} et al., Phys. Lett., A 350, No. 3--4, 221--227 (2006; Zbl 1195.34117) Full Text: DOI References: [1] Bélair, J.; Campbell, S., SIAM J. Appl. Math., 54, 1402 (1994) [2] Campbell, S.; Bélair, J., Can. Appl. Math. Quart., 3, 137 (1995) [3] Olien, L.; Bélair, J., Physica D, 102, 349 (1997) [4] Meng, X.; Wei, J., Chaos Solitons Fractals, 21, 729 (2004) [5] Liao, X.; Wong, K.; Leung, C.; Wu, Z., Chaos Solitons Fractals, 12, 1535 (2001) [6] Ucar, A., Chaos Solitons Fractals, 16, 187 (2003) [7] Li, C.; Liao, X.; Yu, J., Chaos Solitons Fractals, 19, 779 (2004) [8] Ueda, Y.; Ohta, H., Chaos, 4, 1 (1994) [9] Sadkowski, A., J. Electroanalytical Chem., 486, 92 (2000) [10] Kowalczyk, R.; Forys, U., Math. Comput. Modelling, 35, 1 (2002) [11] Chen, G.; Dong, C., From Chaos to Order: Methodologies, Perspectives and Applications (1998), World Scientific: World Scientific Singapore [12] Hassard, B.; Kazarinoff, N.; Wan, Y., Theory and Applications of Hopf Bifurcation (1981), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0474.34002 [13] Hale, J.; Verduyn Lunel, S., Introduction to Functional Differential Equations (1993), Springer: Springer New York · Zbl 0787.34002 [14] Kuang, Y., Delay Differential Equations with Applications in Population Dynamics (1993), Academic Press · Zbl 0777.34002 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.