Parametric Analysis and Impulsive Synchronization of Fractional-Order Newton-Leipnik Systems

Abstract

In this paper, the influences of parameters on the dynamics of a fractional-order Newton-Leipnik system were numerically studied. Impulsive synchronization of two fractional-order Newton-Leipnik systems was also investigated. The ranges of the parameters used in this study were relatively broad. The system displayed comprehensive dynamic behaviours, such as fixed points, periodic motion (including periodic-3 motion), chaotic motion, and transient chaos. A period-doubling route to chaos in this study was also found. Sufficient conditions on synchronization of the two systems are provided and illustrative example is given.

Approximate analytical solutions of fractional Benney–Lin equation by reduced differential transform method and the homotopy perturbation method

“…For the illustration of the methodology of the method, we write the Benney-Lin equation in the standard operator form L(u(x, t)) + R(u(x, t)) + N(u(x, t)) = 0 (7) with initial condition u(x, 0) = ϕ(x) (8) where L(u(x, t)) ≡ ∂ α ∂t α (u(x, t)) is the fractional time derivative operator and R (u(x, t)…”

“…Sheu et al [6] has achieved success in finding lowest order system to yield chaos in the study of the dynamics of a fractional order Newton-Leipnik system [7]. Sheu et al [8], on analyzing the influence of the system parameters on the system dynamics concluded that the appropriate selection of the parameters can restrain or generate chaos.…”

Analytical approach to Boussinesq equation with space‐ and time‐fractional derivatives

“…According to fractal spacetime theory (El Naschie's e-infinity theory), time and space do be discontinuous according, and the fractional model is the 1316 A. YıLDıRıM, S. A. SEZER AND Y. KAPLAN best candidate to describe such problems. Time-fractional equations always behave fascinatingly as illustrated in [13,14].…”

Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen–Lee systems

“…Systems with fractional-order dynamics were proven to exist in different disciplines [1], such as viscoelastic systems [2], electromagnetic waves [3], dielectric polarization [4], quantitative finance [5], and quantum evolution of complex systems [6]. Chaotic phenomena were found in several fractional-order systems, e.g., the fractional Lorenz system [7,8], the fractional Duffing system [9][10][11], the fractional Chua system [12,13], the fractional Chen system [14,15], the fractional van der Pol system [16,17], and the fractional Newton-Leipnik system [18,19].…”