Implementation of multi-step differentialtransformation method for hyperchaotic Rossler system

  • Authors

    • Jafar Biazar Guilan university
    • Tahereh Houlari Guilan university
    • Roxana Asayesh Guilan university
  • Hyperchaotic Rossler system, Differential transformation method, Forth-order Runge Kutta method, Multi-step differential transformation method.
  • In this work, the multi-step differential transformation method (MSDTM) is applied to approximate a solution of the hyperchaotic Rossler system. MSDTM is adapted from the differential transformation method (DTM). In this method, DTM is implemented in each subinterval. Results are compared with a fourth-order Runge Kutta method and a standard DTM. The results show that the MSDTM is an efficient and powerful technique for solving hyperchaotic Rossler systems and this method is more accurate than DTM.

  • References

    1. [1] E. N. Lorenz, “Deterministic non-periodic flowâ€, Journal Of the Atmospheric Sciences, Vol.20, (1963), p.p 130-141.
      [2] O. E. Rossler, “An equation for continuous chaosâ€, ¨ Physics Letters A,Vol. 57, (1976), p.p 397-398.
      [3] Dimitris T. Maris, Dimitris A. Goussis, “The â€hidden†dynamics of the Rossler attractorâ€, Physica D: Nonlinear Phenomena, Vol. 295–296, (2015), p.p 66-90.
      [4] R. Barrio, F. Blesa, A. Dena, S. Serrano, “Qualitative and numerical analysis of the Rossler model: Bifurcations of equilibriaâ€, Computers Mathematics with Applications, Vol. 62, Issue 11, (2011), p.p 4140-4150.
      [5] R. Barrio, F. Blesa, S. Serrano, “Qualitative analysis of the Rossler ¨ equations: Bifurcations of limit cycles and chaotic attractorsâ€, Physica D: Nonlinear Phenomena, Vol. 238, Issue 13, (2009) p.p 1087–1100.
      [6] O. Rossler, “An equation for hyper chaotiâ€, ¨ Phys Lett A, Vol. 71, (1979), p.p 155-7.
      [7] E. Abuteen, S. Momani, A. Alawneh, “Solving the fractional nonlinear Bloch system multi-step generalized differential transformâ€, Computers Mathematics with Applications, Vol. 68, Issue 12, Part A, (2014), p.p 2124-2132.
      [8] A. Arikoglu, I. Ozkol, “Solution of fractional dierential equations by using dierential transform methodâ€, Chaos, Solitons and Fractals, Vol. 34, (2007), p.p 1473-1481.
      [9] M. El-Gamel, M. Abd El-Hady, “Computation of the Eigenvalues and Eigenfunction of Generalized Sturm-Liouville Problems via the Differential Transformation Methodâ€, IJRRAS, Vol. 15, (2013), p.p 259-268.

  • Downloads

  • How to Cite

    Biazar, J., Houlari, T., & Asayesh, R. (2016). Implementation of multi-step differentialtransformation method for hyperchaotic Rossler system. International Journal of Applied Mathematical Research, 6(1), 4-6.