پیوندهای مفید
آمار
| تعداد نشریات | 7 |
| تعداد شماره‌ها | 399 |
| تعداد مقالات | 5,389 |
| تعداد مشاهده مقاله | 5,288,010 |
| تعداد دریافت فایل اصل مقاله | 4,882,745 |
Conservative chaotic flow generated via a pseudo-linear system | ||
| AUT Journal of Modeling and Simulation | ||
| مقاله 4، دوره 51، شماره 2، اسفند 2019، صفحه 111-120 اصل مقاله (1.55 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22060/miscj.2019.15141.5126 | ||
| نویسندگان | ||
| Hamed Ghane* 1؛ Mohammad Bagher Menhaj2 | ||
| 1Isalmic Azad University Bandar-e-Anzali Branch | ||
| 2Editor-in-chief | ||
| چکیده | ||
| Analysis of nonlinear autonomous systems has been a popular field of study in recent decades. As a noticeable nonlinear behavior, chaotic dynamics has been intensively investigated since Lorenz discovered the first physical evidence of chaos in his famous equations. Although many chaotic systems have been ever reported in the literature, a systematic and qualitative approach for chaos generation is still a challenging issue. Recently, we have developed an analysis tool which provides globally valid results about the qualitative behavior of some nonlinear systems based on their pseudolinear form of representation. In this paper, it is applied to generate conservative chaos by focusing on the essential qualitative attribute of conservative chaotic behavior. This feature is the continual stretching and folding of system trajectories which never settle down to a periodic regime. Indeed, it is tried to create this quality of behavior through the aforementioned qualitative analysis tool. The proposed approach helps us to generate a new class of chaotic systems with highly remarkable characteristics. The most elegant one is its almost parameter independency for chaos generation; There is no need for a trial-and-error mechanism to find the exact parameters’ values in order to produce chaotic behavior. It is shown that the system exhibits conservative chaotic dynamics for almost all parameters’ values. The chaotic behavior of the derived system is verified through the analysis of Lyapunov exponents and dimension as well. Besides, the frequency power spectrum analysis is also performed in order to put more emphasis on the chaotic behavior of the system. | ||
| کلیدواژه‌ها | ||
| Chaos Generation؛ Qualitative Analysis؛ Pseudo Linear Systems؛ Nonlinear Eigenvalues؛ Nonlinear Eigenvectors | ||
| مراجع | ||
|
1. Raiesdana, S. and Goplayegani, S.M.H., “Study on chaos anti-control for hippocampal models of epilepsy,” Neurocomputing, 111, pp. 54-69, (2013)
2. L. P. Shilnikov, “On a Poincare–Birkhoff problem,” Mat. Sb. (N.S.), 74(116):3 (1967), 378–397; Math. USSR-Sb., 3:3, 353–371, (1967)
3. Ghane, H. and Menhaj, M. B.: Eigenstructure Based Analysis for Nonlinear Autonomous Systems, IMA J. Math. Control Inf., Vol 32, Issue 1(2013)
4. Ghane, H. and Menhaj, M. B.: Pseudo Linear Systems; Stability Analysis and Limit Cycle Emergence, Journal of Control Engineering and Applied Informatics,16, 78-89(2014)
5. Banks, S. P. and Mhana, K. J.: Optimal control and stabilization of nonlinear systems, IMA J. Math.Control Inf., 9, 179-196. (1992).
6. Liu X., Teo, K., Zhang, H. and Chen, G.: Switching control of linear systems for generating chaos, Chaos, Solitons & Fractals, 30, 723-33, (2006).
7. Wang, X. and Qin, X.: Chaos Generated by Switching Fractional Systems, Mathematical Problems in Engineering, Vol. 2012, 1-15, (2012)
8. Wolf, A., Swift, J. B., Swinney, H. L. and Vastano, J. A.: Determining Lyapunov exponents from a time series, Physica D, Vol. 16, pp. 285-317, (1985).
9. Grasberger, P. and Procaccia, I.: Characterization of strange attractors, Phys. Rev. Lett. 50, 346–349, (1983).
10. Kaplan, J. L. and Yorke, J. A.: Chaotic behavior of multidimensional difference equations, Lecture Notes in Mathematics, Springer – Verlag, 228-237, (1979).
11. Hilborn R. C.: Chaos and Nonlinear Dynamics: An Introduction for Scientists and Engineers, 2ed edition, Oxford Univ. Press, (1994).
12. Arnold, V. I.: Proof of a theorem of A. N. Kolmogorov on the preservation of conditionally periodic motions under a small perturbation of the Hamiltonian, English translation in Russian Math. Surveys 18, 5, 9–36., (1963).
13. Gan, C., Wang, Q. and Perc, M.: Torus breakdown and noise-induced dynamics in the randomly driven Morse oscillator, J. Phys. A: Math. Theor. 43, 125102, (2010).
14. Ghane, H., Sterk, A. And Waalkens, H.: Chaotic dynamics from a pseudo-linear system, IMA J. Math. Control Inf., (2019). | ||
|
آمار تعداد مشاهده مقاله: 377 تعداد دریافت فایل اصل مقاله: 150 |
||