一个四维混沌的广义发电机系统的动力学分析
Dynamic Analysis of a 4D Hyperchaotic Generalized Segmented Disc Dynamo System
摘要: 本文基于segmented disc dynamo发电机，提出了一个新的四维混沌的广义发电机系统。作者研究了Pitchfork分叉、Hopf分叉、zero-zero Hopf分叉，给出了在不同条件下系统存在pitchfork分叉、Hopf分叉和周期解的证明，并给出了Pitchfork分叉和Hopf分叉的数值模拟。
Abstract: Based on segmented disc dynamo, a new four-dimensional chaotic generalized generator system was proposed. The author studies Pitchfork fork, Hopf fork and zero-zero Hopf fork, gives the proof that Pitchfork fork and periodic solution exist in the system under different conditions, and gives the numerical simulation of Pitchfork fork.
文章引用：吴锋. 一个四维混沌的广义发电机系统的动力学分析[J]. 理论数学, 2020, 10(2): 111-127. https://doi.org/10.12677/PM.2020.102018

参考文献

[1] Lorenz, E.N. (1963) Deterministic Nonperiodic Flow. Journal of the Atmospheric Sciences, 20, 130-141. [Google Scholar] [CrossRef] 
[2] Sparrow, C. (1982) The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. Springer, Berlin. [Google Scholar] [CrossRef] 
[3] Hirsch, M., Smale, S. and Devaney, R. (2008) Differential Equations, Dynamical Systems, and an Introduction to Chaos. Elsevier, Singapore.
[4] Robinson, C. (2000) Nonsymmetric Lorenz Attractors from a Homoclinic Bifurcation. SIAM, Journal on Mathematical Analysis, 32, 119-141. [Google Scholar] [CrossRef] 
[5] Yang, Q., Chen, G. and Huang, K. (2007) Chaotic Attractors of the Conjugate Lorenz-Type System. International Journal of Bifurcation and Chaos, 17, 3929-3949. [Google Scholar] [CrossRef] 
[6] Yang, Q. and Chen, G. (2008) A Chaotic System with One Saddle and Two Stable Node-Foci. International Journal of Bifurcation and Chaos, 18, 1393-1414. [Google Scholar] [CrossRef] 
[7] Yang, Q. and Chen, Y. (2014) Complex Dynamics in the Unified Lorenz-Type System. International Journal of Bifurcation and Chaos, 24, Article ID: 1450055. [Google Scholar] [CrossRef] 
[8] Chen, Y. and Yang, Q. (2014) Dynamics of a Hyperchaotic Lorenz-Type System. Nonlinear Dynamics, 77, 569-581. [Google Scholar] [CrossRef] 
[9] Hastings, S. and Troy, W. (1994) A Proof That the Lorenz Equations Have a Homoclinic Orbit. Journal of Differential Equations, 113, 166-188. [Google Scholar] [CrossRef] 
[10] Hastings, S. and Troy, W. (1996) A Shooting Approach to Chaos in the Lorenz Equations. Journal of Differential Equations, 127, 41-53. [Google Scholar] [CrossRef] 
[11] Bullard, E.C. (1955) The Stability of a Homopolar Dynamo. Mathematical Proceedings of the Cambridge Philosophical Society, 51, 744-760. [Google Scholar] [CrossRef] 
[12] Allan, D.W. (1962) On the Behaviour of Systems of Coupled Dynamos. Mathematical Proceedings of the Cambridge Philosophical Society, 58, 671-693. [Google Scholar] [CrossRef] 
[13] Cook, A.E. and Roberts, P.H. (1970) The Rikitake Two-Disc Dynamo System. Mathematical Proceedings of the Cambridge Philosophical Society, 68, 547-569. [Google Scholar] [CrossRef] 
[14] Ito, K. (1980) Chaos in the Rikitake Two-Disc Dynamo System. Earth and Planetary Science Letters, 51, 451-456. [Google Scholar] [CrossRef] 
[15] Robbins, K.A. (1977) A New Approach to Subcritical Instability and Turbulent Transitions in a Simple Dynamo. Mathematical Proceedings of the Cambridge Philosophical Society, 82, 309-325. [Google Scholar] [CrossRef] 
[16] Moffatt, H.K. (1979) A Self-Consistent Treatment of Simple Dynamo Systems. Geophysical & Astrophysical Fluid Dynamics, 14, 147-166. [Google Scholar] [CrossRef] 
[17] Wiggins, S. (1990) Introduction to Applied Nonlinear Dynamical Systems and Chaos. Springer, New York, 200-253. [Google Scholar] [CrossRef] 
[18] Wang, J.Z., Zhang, Q. and Chen, Z.Q. (2014) Local Bifurcation Analysis and Ultimate Bound of a Novel 4D Hyper-Chaotic System. Nonlinear Dynamics, 78, 2517-2531. [Google Scholar] [CrossRef] 
[19] Wu, W.J., Chen, Z.Q. and Yuan, Z.Z. (2008) Local Bifurcation Analysis of a Four-Dimensional Hyperchaotic System. Chinese Physics B, 17, 2420-2432. [Google Scholar] [CrossRef] 
[20] Li, X. and Wang, P. (2013) Hopf Bifurcation and Heteroclinic Orbit in a 3D Autonomous Chaotic System. Nonlinear Dynamics, 73, 621-632. [Google Scholar] [CrossRef] 
[21] Wang, Z.L., Zhou, L.L., Chen, Z.Q. and Wang, J.Z. (2015) Local Bifurcation Analysis and Topological Horseshoe of a 4D Hyperchaotic System. Nonlinear Dynamics, 83, 2055-2066. [Google Scholar] [CrossRef] 
[22] Li, D., Lu, J., Wu, X. and Chen, G. (2006) Estimating the Ultimate Bound and Positively Invariant Set of the Lorenz System and a Unied Chaotic System. Journal of Mathematical Analysis and Applications, 323, 844-853. [Google Scholar] [CrossRef] 
[23] Wang, P., Li, D. and Hu, Q. (2010) Bounds of the Hyper-Chaotic Lorenz-Stenflo System. Communications in Nonlinear Science and Numerical Simulation, 15, 2514-2520. [Google Scholar] [CrossRef] 
[24] Zhang, F., Mu, C. and Li, X. (2012) On the Boundness of Some Solutions of the Lü System. International Journal of Bifurcation and Chaos, 22, 1250015-1250050. [Google Scholar] [CrossRef] 
[25] Zhang, F., Mi, C., Wang, L., Wang, X. and Yao, X. (2014) Estimations for Ultimate Boundary of a New Hyperchaotic System and Its Simulation. Nonlinear Dynamics, 75, 529-537. [Google Scholar] [CrossRef] 
[26] Wang, P., Li, D., Wu, X., Yu, X., et al. (2011) Ultimate Bound Estimation of a Class of High Dimensional Quadratic Autonomous Dynamical Systems. International Journal of Bifurcation and Chaos, 21, 2679-2694. [Google Scholar] [CrossRef] 

为你推荐