Journal ArticleDOI
Chaos in the Newton–Leipnik system with fractional order
Long-Jye Sheu,Hsien-Keng Chen,Juhn-Horng Chen,Lap Mou Tam,Wen-Chin Chen,Kuang-Tai Lin,Yuan Kang +6 more
Reads0
Chats0
TLDR
In this article, the dynamics of the Newton-Leipnik system with fractional order was studied numerically, and it was found that chaos exists in the fractional-order system with order less than 3.Abstract:
The dynamics of fractional-order systems has attracted increasing attention in recent years. In this paper, the dynamics of the Newton–Leipnik system with fractional order was studied numerically. The system displays many interesting dynamic behaviors, such as fixed points, periodic motions, chaotic motions, and transient chaos. It was found that chaos exists in the fractional-order system with order less than 3. In this study, the lowest order for this system to yield chaos is 2.82. A period-doubling route to chaos in the fractional-order system was also found.read more
Citations
More filters
Journal ArticleDOI
A necessary condition for double scroll attractor existence in fractional-order systems
TL;DR: Based on the stability theorem in fractional differential equations, a necessary condition is given to check existence of double scroll attractor in a fractional-order system as mentioned in this paper, and numerical simulations are presented to evaluate accuracy of this condition.
Journal ArticleDOI
Chaotic attractors in incommensurate fractional order systems
TL;DR: In this paper, a necessary condition is given to check the existence of 1-scroll, 2-scroll or multi-scroll chaotic attractors in a fractional order system, based on the stability theorems in fractional differential equations.
Journal ArticleDOI
Synchronization of chaotic fractional-order systems via active sliding mode controller
TL;DR: In this article, a controller based on active sliding mode theory is proposed to synchronize chaotic fractional-order systems in master-slave structure, where master and slave systems may be identical or different.
Journal ArticleDOI
Synchronization of fractional order chaotic systems using active control method
TL;DR: In this article, the active control method is used for synchronization of two different pairs of fractional order systems with Lotka-Volterra chaotic system as the master system and the other two fractional-order chaotic systems, viz., Newton-Leipnik and Lorenz systems as slave systems separately.
Journal ArticleDOI
Sliding mode synchronization of an uncertain fractional order chaotic system
TL;DR: It has been shown that, not only the performance of the proposed method is satisfying with an acceptable level of control signal, but also a rather simple stability analysis is performed.
References
More filters
Book
Applications Of Fractional Calculus In Physics
TL;DR: An introduction to fractional calculus can be found in this paper, where Butzer et al. present a discussion of fractional fractional derivatives, derivatives and fractal time series.
Journal ArticleDOI
Linear Models of Dissipation whose Q is almost Frequency Independent-II
TL;DR: In this paper, a linear dissipative mechanism whose Q is almost frequency independent over large frequency ranges has been investigated by introducing fractional derivatives in the stressstrain relation, and a rigorous proof of the formulae to be used in obtaining the analytic expression of Q is given.
Journal ArticleDOI
Analysis of Fractional Differential Equations
Kai Diethelm,Neville J. Ford +1 more
TL;DR: In this paper, the authors discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order, and investigate the dependence of the solution on the order of the differential equation and on the initial condition.
Book
A Predictor-Corrector Approach for the Numerical Solution of Fractional Differential Equations
TL;DR: In this paper, an Adams-type predictor-corrector method for the numerical solution of fractional differential equations is discussed, which may be used both for linear and nonlinear problems, and it may be extended tomulti-term equations (involving more than one differential operator) too.