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

K. Moaddy; I. Hashim; S. Momani

doi:10.1016/j.camwa.2011.03.059

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

K. Moaddy
, I. Hashim
, S. Momani

Universiti Kebangsaan Malaysia
University of Jordan

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

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 language	English
Pages (from-to)	1068-1074
Number of pages	7
Journal	Computers and Mathematics with Applications
Volume	62
Issue number	3
DOIs	https://doi.org/10.1016/j.camwa.2011.03.059
State	Published - Aug 2011
Externally published	Yes

Keywords

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

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10.1016/j.camwa.2011.03.059

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title = "Non-standard finite difference schemes for solving fractional-order R{\"o}ssler chaotic and hyperchaotic systems",

abstract = "In this paper, the non-standard finite difference method (for short NSFD) is implemented to study the dynamic behaviors in the fractional-order R{\"o}ssler 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 R{\"o}ssler 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.",

keywords = "Chaos, Fractional differential equations, Non-standard finite deference schemes, R{\"o}ssler system",

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TY - JOUR

T1 - Non-standard finite difference schemes for solving fractional-order Rössler chaotic and hyperchaotic systems

AU - Moaddy, K.

AU - Hashim, I.

AU - Momani, S.

PY - 2011/8

Y1 - 2011/8

N2 - 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.

AB - 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.

KW - Chaos

KW - Fractional differential equations

KW - Non-standard finite deference schemes

KW - Rössler system

UR - https://www.scopus.com/pages/publications/79961000780

U2 - 10.1016/j.camwa.2011.03.059

DO - 10.1016/j.camwa.2011.03.059

M3 - Article

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SN - 0898-1221

VL - 62

SP - 1068

EP - 1074

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 3

ER -

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

Abstract

Keywords

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