Non-standard finite difference schemes for solving fractional-order Rössler chaotic and hyperchaotic systems

K. Moaddy, Ishak Hashim, S. Momani

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

In this paper, the non-standard finite difference method (for short NSFD) is implemented to study the dynamic behaviors in the fractional-order Rössler chaotic and hyperchaotic systems. The GrnwaldLetnikov method is used to approximate the fractional derivatives. We found that the lowest value to have chaos in this system is 2.1 and hyperchaos exists in the fractional-order Rössler system of order as low as 3.8. Numerical results show that the NSFD approach is easy to implement and accurate when applied to differential equations of fractional order.

Original languageEnglish
Pages (from-to)1068-1074
Number of pages7
JournalComputers and Mathematics with Applications
Volume62
Issue number3
DOIs
Publication statusPublished - Aug 2011

Fingerprint

Nonstandard Finite Difference Schemes
Hyperchaotic System
Fractional-order System
Finite difference method
Chaos theory
Chaotic System
Differential equations
Hyperchaos
Derivatives
Fractional Derivative
Fractional Order
Dynamic Behavior
Difference Method
Lowest
Finite Difference
Chaos
Differential equation
Numerical Results

Keywords

  • Chaos
  • Fractional differential equations
  • Non-standard finite deference schemes
  • Rössler system

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Modelling and Simulation
  • Computational Mathematics

Cite this

Non-standard finite difference schemes for solving fractional-order Rössler chaotic and hyperchaotic systems. / Moaddy, K.; Hashim, Ishak; Momani, S.

In: Computers and Mathematics with Applications, Vol. 62, No. 3, 08.2011, p. 1068-1074.

Research output: Contribution to journalArticle

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