Li, TieCheng; Chen, Guanrong; Tang, Yun On stability and bifurcation of Chen’s system. (English) Zbl 1069.34060 Chaos Solitons Fractals 19, No. 5, 1269-1282 (2004). Summary: This article investigates some subtle characteristics of stability and bifurcation of the chaotic Chen’s system, based on rigorous mathematical analysis and symbolic computations. Cited in 34 Documents MSC: 34C23 Bifurcation theory for ordinary differential equations 34D20 Stability of solutions to ordinary differential equations PDF BibTeX XML Cite \textit{T. Li} et al., Chaos Solitons Fractals 19, No. 5, 1269--1282 (2004; Zbl 1069.34060) Full Text: DOI References: [1] Agiza, H. N.; Yassen, M. T., Synchronization of Rössler and Chen chaotic dynamical systems using active control, Phys. Lett. A, 278, 191-197 (2001) · Zbl 0972.37019 [2] C̆elikovský, S.; Chen, G., On a generalized Lorenz canonical form of chaotic systems, Int. J. Bifurcat. Chaos, 12, 1789-1812 (2002) · Zbl 1043.37023 [3] Chen, G., Controlling chaos and bifurcations in engineering systems (1999), CRC Press: CRC Press Boca Raton [4] Chen, G., Chaotification via feedback: the discrete case, (Chen, G.; Yu, X., Chaos control: theory and applications (2003), Springer-Verlag: Springer-Verlag Heidelburg), 159-178 · Zbl 1330.93107 [5] Chen, G.; Dong, X., From chaos to order: methodologies. perspectives and applications (1998), World Scientific: World Scientific Singapore [6] Chen, G.; Lai, D., Anticontrol of chaos via feedback, Int. J. Bifurcat. Chaos, 8, 1585-1590 (1998) · Zbl 0941.93522 [7] Chen, S. H.; Lü, J., Synchronization of an uncertain unified chaotic system via adaptive control, Chaos, Solitons & Fractals, 14, 643-647 (2002) · Zbl 1005.93020 [8] Guan, X. P.; Fan, Z. P.; Peng, H. P.; Wang, Y. Q., The adaptive control of Chen’s chaotic systems, Acta Phys. Sinica, 50, 2108-2111 (2001) [9] Guan, Z. H.; Liao, R. Q.; Zhou, F.; Wang, H. O., On impulsive control and its application to Chen’s chaotic systems, Int. J. Bifurcat. Chaos, 12, 1191-1197 (2002) · Zbl 1051.93508 [10] Kuznetsov, Y. A., Elements of applied bifurcation theory (1995), Springer-Verlag: Springer-Verlag New York · Zbl 0829.58029 [11] Li, C.; Chen, G., A note on Hopf bifurcation in Chen’s system, Int J Bifurcat Chaos, 13, 1609-1615 (2003) · Zbl 1074.34045 [13] Lu, J. A.; Lü, J.; Chen, S. H., Chen’s chaotic attractor and its characteristic quantity, Contr. Theory Appl., 19, 308-310 (2002) · Zbl 1011.37019 [14] Lü, J.; Chen, G.; Cheng, D.; C̆elikovský, S., Bridge the gap between the Lorenz system and the Chen system, Int. J. Bifurcat. Chaos, 12, 2917-2926 (2002) · Zbl 1043.37026 [15] Lü, J.; Chen, G.; Zhang, S., Controlling in between the Lorenz and the Chen systems, Int. J. Bifurcat. Chaos, 12, 1417-1422 (2002) [16] Lü, J.; Zhang, S., Controlling Chen’s chaotic attractor using backstepping design based on parameters identification, Phys. Lett. A, 286, 148-152 (2001) · Zbl 0969.37509 [17] Lü, J.; Zhou, T.; Chen, G.; Zhang, S., Local bifurcation of the Chen system, Int. J. Bifurcat. Chaos, 12, 2257-2270 (2002) · Zbl 1047.34044 [18] Lü, J.; Zhou, T.; Zhang, S., Chaos synchronization between linearly coupled chaotic systems, Chaos, Solitons & Fractals, 14, 529-541 (2002) · Zbl 1067.37043 [19] Lü, J.; Zhou, T.; Zhang, S., Controlling Chen’s chaotic attractor using feedback function based on parameters identification, Chinese Phys., 11, 12-16 (2002) [20] Luo, D., Bifurcation theory and methods of dynamical systems (1997), World Scientific: World Scientific Singapore [21] Ueta, T.; Chen, G., Bifurcation analysis of Chen’s attractor, Int. J. Bifurcat. Chaos, 10, 1917-1931 (2002) · Zbl 1090.37531 [22] Wang, X., Chen’s attractor-A new chaotic attractor, Contr. Theory Appl., 16, 779 (2000) [23] Wang, X.; Chen, G., Chaotification via arbitrarily small feedback controls, Int. J. Bifurcat. Chaos, 10, 549-570 (2000) · Zbl 1090.37532 [24] Wang, X.; Chen, G.; Yu, X., Anticontrol of chaos in continuous-time systems via time-delayed feedback, Chaos, 10, 771-779 (2000) · Zbl 0967.93045 [25] Yang, B. L.; Yang, T., Sampled data feedback control of Chen’s system, Acta Phys. Sinica, 49, 1039-1042 (2000) [26] Yassen, M. T., Chaos control of Chen chaotic dynamical system, Chaos, Solitons & Fractals, 15, 271-283 (2003) · Zbl 1038.37029 [27] Yu, X.; Xia, Y., Detecting unstable periodic orbits in Chen’s chaotic attractor, Int. J. Bifurcat. Chaos, 10, 1987-1991 (2001) [28] Zhong, G. Q.; Tang, K. S., Circuitry implementation and synchronization of Chen’s attractor, Int. J. Bifurcat. Chaos, 12, 1423-1427 (2002) 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.