Boundedness of Certain Forms of Jerky Dynamics A

• Autores: Zeraoulia Elhadj, J.C. Sprott
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 11, Nº 2, 2012, págs. 199-213
• Idioma: inglés
• Enlaces
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• Resumen

  • In this paper, we find regions in the bifurcation parameter space of certain forms of jerky dynamic systems where they are bounded. The method of analysis is based on a recent result about the boundedness of solutions of a certain type of third-order nonlinear differential equation with bounded delay. In particular, the boundedness of some chaotic attractors displayed by these systems is confirmed analytically.

• Referencias bibliográficas
  • Sprott J.C.: Some simple chaotic flows. Phys. Rev. E 50, R647–R650 (1994)
  • Sprott J.C.: Some simple chaotic jerk functions. Am. J. Phys. 65, 537–543 (1997) Sprott J.C.: Simplest dissipative chaotic flow. Phys. Lett....
  • Moore D.W., Spiegel E.A.: A thermally excited nonlinear oscillator. Astrophys. J. 143, 871–887 (1966)
  • Tunc C.: Bound of solutions to third-order nonlinear differential equations with bounded delay. J. Frankl. Inst. 347, 415–425 (2010)
  • Chen G.: Controlling Chaos and Bifurcations in Engineering Systems. CRC Press, Boca Raton (1999) Leonov G., Bunin A., Koksch N.: Attractor...
  • Sun Y.: Solution bounds of generalized Lorenz chaotic systems. Chaos Solitons Fractals 40, 691–696 (2009) Li D., Lu J.A., Wu X., Chen G.:...
  • Zeraoulia E., Sprott J.C.: About the boundedness of 3D continuous-time quadratic systems. Nonlinear Oscillations 13(4), 1–8 (2010)
  • Eichhorn R., Linz S.J., Hanggi P.: Transformations of nonlinear dynamical systems to jerky motion and its application to minimal chaotic flows....
  • El’sgol’ts, L.E.: Introduction to the theory of differential equations with deviating arguments [translated from the Russian by Robert J....
  • Zhou T., Chen G.: Classification of chaos in 3-D autonomous quadratic systems-I Basic framework and methods. Int. J. Bifurc. Chaos 16, 2459–2479...