TY - GEN
T1 - Parametric Control on Fractional-Order Response for Lü Chaotic System
AU - Moaddy, K
AU - Radwan, A G
AU - Salama, Khaled N.
AU - Momani, S
AU - Hashim, I
N1 - KAUST Repository Item: Exported on 2020-10-01
PY - 2013/4/10
Y1 - 2013/4/10
N2 - This paper discusses the influence of the fractional order parameter on conventional chaotic systems. These fractional-order parameters increase the system degree of freedom allowing it to enter new domains and thus it can be used as a control for such dynamical systems. This paper investigates the behaviour of the equally-fractional-order Lü chaotic system when changing the fractional-order parameter and determines the fractional-order ranges for chaotic behaviour. Five different parameter values and six fractional-order cases are discussed through this paper. Unlike the conventional parameters, as the fractional-order increases the system response begins with stability, passing by chaotic behaviour then reaches periodic response. As the system parameter α increases, a shift in the fractional order is required to maintain chaotic response.Therefore, the range of chaotic response can be expanded or minimized by controlling the fractional-order parameter. The non-standard finite difference method is used to solve the fractional-order Lü chaotic system numerically to validate these responses.
AB - This paper discusses the influence of the fractional order parameter on conventional chaotic systems. These fractional-order parameters increase the system degree of freedom allowing it to enter new domains and thus it can be used as a control for such dynamical systems. This paper investigates the behaviour of the equally-fractional-order Lü chaotic system when changing the fractional-order parameter and determines the fractional-order ranges for chaotic behaviour. Five different parameter values and six fractional-order cases are discussed through this paper. Unlike the conventional parameters, as the fractional-order increases the system response begins with stability, passing by chaotic behaviour then reaches periodic response. As the system parameter α increases, a shift in the fractional order is required to maintain chaotic response.Therefore, the range of chaotic response can be expanded or minimized by controlling the fractional-order parameter. The non-standard finite difference method is used to solve the fractional-order Lü chaotic system numerically to validate these responses.
UR - http://hdl.handle.net/10754/554375
UR - http://stacks.iop.org/1742-6596/423/i=1/a=012024?key=crossref.9726e96550103fd029913f0cbdd54cac
UR - http://www.scopus.com/inward/record.url?scp=84876821667&partnerID=8YFLogxK
U2 - 10.1088/1742-6596/423/1/012024
DO - 10.1088/1742-6596/423/1/012024
M3 - Conference contribution
SP - 012024
BT - Journal of Physics: Conference Series
PB - IOP Publishing
ER -