- 期刊
- OpenAccess
Analysis of a Fractional Order Nonlinear System Based on the Frequency Domain Approximation
並列摘要
The dynamics of nonlinear system is very complicated especially the fractional nonlinear system since they can be found in many areas of engineering and science. The dynamics of the Lorenz system with fractional derivatives is analysed based on the frequency approximation. For a given range of parameters where the non‐fractional Lorenz system has periodic orbits, it is found that the fractional Lorenz system exhibits chaos and hyperchaos. A striking finding is that the fractional Lorenz system exhibits hyperchaos, although the total system order is less than 3, which is contrary to the well known conclusion that hyperchaos cannot occur in the integer‐order continuous‐time autonomous system of order less than 4. Finally, a reasonable explanation is offered for this complicated dynamical phenomenon.
延伸閱讀
- Li, M., Cattani, C., Scalia, M., Lim, S. C., & Chen, W. S. (2014). Dynamical Processes and Systems of Fractional Order. Advances in Mathematical Physics, (2014), 128-129. https://doi.org/10.1155/2014/272493
- FENG, W. (1997). A NEW SPECTRAL THEORY FOR NONLINEAR OPERATORS AND ITS APPLICATIONS. Abstract and Applied Analysis, 1997(), 163-183. https://doi.org/10.1155/S1085337597000328
- Unlu, C., Jafari, H., & Baleanu, D. (2013). Revised Variational Iteration Method for Solving Systems of Nonlinear Fractional-Order Differential Equations. Abstract and Applied Analysis, 2013(), 280-286-532. https://doi.org/10.1155/2013/461837
- Liu, K., & Jiang, W. (2014). Stability of Nonlinear Fractional Neutral Differential Difference Systems. Discrete Dynamics in Nature and Society, 2014(), 355-362-134. https://doi.org/10.1155/2014/514631
- Wang, H., Liu, L., & Tan, Y. (2014). Dynamics of Third-Order Nonlinear Neutral Equations. Discrete Dynamics in Nature and Society, 2014(), 705-708-264. https://doi.org/10.1155/2014/917913