التكامل الداربوكس لتعميم النظام الفوضوي الثلاثي الأبعاد Sprott ET9
محتوى المقالة الرئيسي
الملخص
في هذا البحث تم دراسة التكامل الاول من نوع داربوكس لتعميم النظام الفوضوي الثلاثي الابعاد Sprott ET9 . حيث وضحنا ان النظام لايمتلك متعددة حدود . دالة كسرية, تحليلية والداربوكس للتكامل الاول لاي قيمتين a و b. كما استطعنا ابجاد متعددة حدود داربوكس لهذا النظام بقرب المفكوك الاسي. باستخدام وزن متعددة الحدود المتجانسة التي ساعدتنا في برهان الطريقة.
تفاصيل المقالة
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كيفية الاقتباس
المراجع
Lu J, Chen G. A new chaotic attractor coined. Int J Bifurc Chaos. 2002;12(3):659–61.
Jalal AA, Amen AI, Sulaiman NA. Darboux integrability of the simple chaotic flow with a line equilibria differential system. Chaos, Solitons and Fractals [Internet]. 2020;135:109712. Available from: https://doi.org/10.1016/j.chaos.2020.109712
Jafari S, Sprott JC, Molaie M. A Simple Chaotic Flow with a Plane of Equilibria. Int J Bifurc Chaos. 2016;26(6):1–6.
Barati K, Jafari S, Sprott JC, Pham VT. Simple Chaotic Flows with a Curve of Equilibria. Int J Bifurc Chaos. 2016;26(12):1–6.
Barreira L, Valls C, Llibre J. Integrability and limit cycles of the Moon-Rand system. Int J Non Linear Mech [Internet]. 2015;69:129–36. Available from: http://dx.doi.org/10.1016/j.ijnonlinmec.2014.11.029
Llibre J, Oliveira R, Valls C. On the Darboux integrability of a three–dimensional forced–damped differential system. J Nonlinear Math Phys. 2017;24(4):473–94.
Zhang L, Yu J. Invariant algebraic surfaces of the FitzHugh-Nagumo system. J Math Anal Appl [Internet]. 2019;(November 2018). Available from: https://doi.org/10.1016/j.jmaa.2019.04.009
Oliveira R, Valls C. Global dynamical aspects of a generalized Chen–Wang differential system. Nonlinear Dyn. 2016;84(3):1497–516.
Sprott JC. Some simple chaotic flows. Phys Rev E [Internet]. 1994 Aug 1;50(2):R647–50. Available from: https://link.aps.org/doi/10.1103/PhysRevE.50.R647
Posch HA, Hoover WG, Vesely FJ. Canonical dynamics of the Nosé oscillator: Stability, order, and chaos. Phys Rev A [Internet]. 1986 Jun 1;33(6):4253–65. Available from: https://link.aps.org/doi/10.1103/PhysRevA.33.4253
Hoover WG. Canonical dynamics: Equilibrium phase-space distributions. Phys Rev A [Internet]. 1985 Mar 1;31(3):1695–7. Available from: https://link.aps.org/doi/10.1103/PhysRevA.31.1695
Messias M, Reinol AC. On the existence of periodic orbits and KAM tori in the Sprott A system: a special case of the Nosé–Hoover oscillator. Nonlinear Dyn [Internet]. 2018;92(3):1287–97. Available from: https://doi.org/10.1007/s11071-018-4125-1
Oliveira R, Valls C. Chaotic behavior of a generalized Sprott E differential dystem. Int J Bifurc Chaos. 2016;26(5):1–16.
Mahdi A, Valls C. Integrability of the Nosé-Hoover equation. J Geom Phys [Internet]. 2011;61(8):1348–52. Available from: http://dx.doi.org/10.1016/j.geomphys.2011.02.018
Sprott JC. Strange attractors with various equilibrium types. Eur Phys J Spec Top. 2015;224(8):1409–19.
Wang MJ, Liao XH, Deng Y, Li ZJ, Zeng YC, Ma ML. Bursting, Dynamics, and Circuit Implementation of a New Fractional-Order Chaotic System with Coexisting Hidden Attractors. J Comput Nonlinear Dyn. 2019;14(7):1–12.
Akgul A, Moroz I, Pehlivan I, Vaidyanathan S. A new four-scroll chaotic attractor and its engineering applications. Optik (Stuttg) [Internet]. 2016;127(13):5491–9. Available from: http://dx.doi.org/10.1016/j.ijleo.2016.02.066
Moysis L, Volos C, Pham V, Goudos S, Stouboulos I, Gupta MK, et al. Analysis of a Chaotic System with Line Equilibrium and Its Application to Secure Communications Using a Descriptor Observer †. Technologies. 2019;7(4):76.
Sambas A, Vaidyanathan S, Mamat M, Sanjaya Ws M, Yuningsih SH, Zakaria K. Analysis, Control and Circuit Design of a Novel Chaotic System with Line Equilibrium. J Phys Conf Ser. 2018;1090(1).
Dumortier F, Llibre J, Artés JC. Qualitative theory of planar differential systems. Springer, Berlin, Heidelberg; 2006.
Canada A, Drabek P, Fonda A. Handbook of Differential Equations Ordinary Differential Equations. 1st ed. Netherlands: Elsevier B.V; 2004. 708 p.
Llibre J, Valls C. Darboux integrability of generalized Yang-Mills Hamiltonian system. J Nonlinear Math Phys [Internet]. 2016;23(2):234–42. Available from: https://doi.org/10.1080/14029251.2016.1175820
Llibre J, Valls C. On the Darboux integrability of the Painlevé II equations. J Nonlinear Math Phys [Internet]. 2015;22(1):60–75. Available from: http://dx.doi.org/10.1080/14029251.2015.996441
Llibre J, Zhang X. Darboux theory of integrability in Cn taking into account the multiplicity. J Differ Equ [Internet]. 2009;246(2):541–51. Available from: http://dx.doi.org/10.1016/j.jde.2008.07.020
Llibre J, Yu J, Zhang X. On polynomial integrability of the Euler equations on so(4). J Geom Phys [Internet]. 2015;96:36–41. Available from: http://dx.doi.org/10.1016/j.geomphys.2015.06.001
Zhang X. Integrability of Dynamical Systems: Algebra and Analysis [Internet]. Vol. 47. Singapore Springer; 2017. Available from: http://link.springer.com/10.1007/978-981-10-4226-3
Zhang X. Liouvillian integrability of polynomial differential systems. Am Math Soc. 2016;368(1):607–20.
Darboux G. Mémoire sur les équations différentielles algébriques du premier ordre et du premier degré. 1878;2(1):60–96.
Fraleigh JB. A first course in abstract algebra [Internet]. seventh ed. Vol. 3. Pearson Education Limited; 2014. 461 p. Available from: https://www.amazon.com/First-Course-Abstract-Algebra-7th/dp/B009NGC1UO
Christopher C, Llibre J, Pereira JV. Multiplicity of Invariant Algebraic Curves in Polynomial Vector Fields. Pacific J Math [Internet]. 2007;229(1):63–117. Available from: 34C05
Christopher C, Llibre J, Pantazi C, Walcher S. On planar polynomial vector fields with elementary first integrals. J Differ Equ [Internet]. 2019;267(8):4572–88. Available from: https://doi.org/10.1016/j.jde.2019.05.007
Li W, Llibre J, Zhang X. Local first integrals of differential systems equations and diffeomorphism. Zeitschrift für Angew Math und Phys ZAMP. 2003;54(2):235–55.
Llibre J, Zhang X. Darboux theory of integrability for polynomial vector fields in Rn taking into account the multiplicity at infinity. Bull des Sci Math [Internet]. 2009;133(7):765–78. Available from: http://dx.doi.org/10.1016/j.bulsci.2009.06.002
Llibre J, Audia CL. On the integrability of the 5-dimensional lorenz system for the Gravity-Wave activity. Proceedings of the American Mathematical Society.2017;145(2):665–79.
Lü T, Zhang X. Darboux polynomials and algebraic integrability of the Chen system. Int J Bifurc Chaos. 2007;17(8):2739–48.