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 ? 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. © IOP Publishing Ltd 2013.
Moaddy K., Radwan A.G., Salama K.N., Momani S., Hashim I.
Chaos theory; Degrees of freedom (mechanics); Dynamical systems; Finite difference method; Chaotic behaviour; Chaotic response; Degree of freedom; Fractional order; Non-standard finite-differences; Parametric control; Periodic response; System response; Chaotic systems
Journal of Physics: Conference Series, Vol. 423, Art. No. 12024, Doi: 10.1088/1742-6596/423/1/012024