49
Views
2
CrossRef citations to date
0
Altmetric
Articles

On the global dynamics of a three-dimensional forced-damped differential system

, &
Pages 414-428 | Received 30 Apr 2019, Accepted 14 Oct 2019, Published online: 04 May 2020

References

  • A. Cima and J. Llibre, Bounded polynomial systems, Trans. Amer. Math. Soc., 318 (1990), 557–579. doi: 10.1090/S0002-9947-1990-0998352-5
  • A. Craig and H. Okamoto, A three-dimensional autontomous system with unbounded bending solu- tions, Physica D, 164 (2002), 168–186. doi: 10.1016/S0167-2789(02)00372-X
  • F. Dumortier, J. Llibre and J.C. Artés, Qualitative theory of planar differential systems, (Universitext, Spring-Verlag, 2006).
  • J. Llibre, R. Oliveira and C. Valls, On the Darboux integrability of a three-dimensional forced-damped differential system, J. Nonlinear Math. Phys., 24 (2017), 473–494. doi: 10.1080/14029251.2017.1375686
  • N.G. Lloyd, Degree Theory, (Cambridge University Press, 1978).
  • E.N. Lorenz, Deterministic nonperiodic flow, J. Atmos. Sci., 20 (1963), 130–141. doi: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
  • T. Miyaji, H. Okamoto and A. Craig, A Four-Leaf chaotic attractor of a three-dimensional dyamical system, Internat. J. Bifur. Chaos. Appl. Sci. Engrg., 25 (2015), 1530003, pp. 21. doi: 10.1142/S0218127415300037
  • T. Miyaji, H. Okamoto and A. Craig, Three-dimensional forced-damped dynamical system with rich dynamics: Bifurcations, chaos and unbounded solutions, Physica D, 311-312 (2015), 25–36. doi: 10.1016/j.physd.2015.09.001
  • I. Pehlivan, Four-scroll stellate new chaotic system, Optoelectronics and Advanced materials–rapid communications, 5 (2011), 1003–1006.
  • H. Poincaré, Mémoire sur les courbes définies par une équation différentielle, J. Maths. Pures Appl., 7 (1881), 375–422, 1881.
  • A. Russell, A Treatise on differential equations, (Macmillan and Co, London, 1885).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.