Implementation of multi-step differentialtransformation method for hyperchaotic Rossler system
DOI:
https://doi.org/10.14419/ijamr.v6i1.6875Published:
2016-12-23Keywords:
Hyperchaotic Rossler system, Differential transformation method, Forth-order Runge Kutta method, Multi-step differential transformation method.Abstract
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] 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.
License
Authors who publish with this journal agree to the following terms:
                          [1]           Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
                          [2]           Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
                          [3]           Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).