Dynamic analysis of nonlinear variable frequency water supply system with time delay
作者： Yuting Ding
DOI: 10.1007/S11071-017-3681-0
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摘要: In this paper, we study the mathematical model about variable frequency water supply system in process of applying glue to particleboard. Based on original linear ordinary differential model, effects time delay and nonlinear factor are considered. Then, obtain delayed equation associated with system. Further, consider existence stability equilibria several types bifurcations functional equation. Next, derive normal forms Hopf bifurcation Bogdanov–Takens by using multiple scales method center manifold reduction method, respectively, analyze classifications local dynamics. Finally, Matlab software, numerical simulations estimated values parameters show stable equilibrium, periodic-1, periodic-2, periodic-4 solutions, a complex chaotic attractor from sequence period-doubling bifurcations.
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sci-hub.se 参考文章(28)
Yuri A. Kuznetsov, Elements of applied bifurcation theory ,(1995)
Ulrich Hundhausen, Holger Militz, Carsten Mai, Use of alkyl ketene dimer (AKD) for surface modification of particleboard chips European Journal of Wood and Wood Products. ,vol. 67, pp. 37- 45 ,(2009) , 10.1007/S00107-008-0275-Z
S. L. Das, A. Chatterjee, Multiple scales without center manifold reductions for delay differential equations near Hopf bifurcations Nonlinear Dynamics. ,vol. 30, pp. 323- 335 ,(2002) , 10.1023/A:1021220117746
'Alī Hasan Nā'ifa, Introduction to perturbation techniques ,(1981)
Anael Verdugo, Mathematical analysis of a biochemical oscillator with delay Journal of Computational and Applied Mathematics. ,vol. 291, pp. 66- 75 ,(2016) , 10.1016/J.CAM.2015.04.029
Stephen Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos ,(1989)
T. Faria, L.T. Magalhaes, Normal Forms for Retarded Functional Differential Equations with Parameters and Applications to Hopf Bifurcation Journal of Differential Equations. ,vol. 122, pp. 181- 200 ,(1995) , 10.1006/JDEQ.1995.1144
Yong Xu, Yongge Li, Di Liu, Wantao Jia, Hui Huang, Responses of Duffing oscillator with fractional damping and random phase Nonlinear Dynamics. ,vol. 74, pp. 745- 753 ,(2013) , 10.1007/S11071-013-1002-9
T. Faria, L.T. Magalhaes, Normal Forms for Retarded Functional Differential Equations and Applications to Bogdanov-Takens Singularity Journal of Differential Equations. ,vol. 122, pp. 201- 224 ,(1995) , 10.1006/JDEQ.1995.1145
Hongbin Wang, Weihua Jiang, Yuting Ding, Bifurcation phenomena and control analysis in class-B laser system with delayed feedback Nonlinear Dynamics. ,vol. 79, pp. 2421- 2438 ,(2015) , 10.1007/S11071-014-1822-2