2,859 research outputs found
Synchronization of Uncertain Fractional-Order Duffing-Holmes Chaotic System via Sliding Mode Control
In this paper, a sliding mode controller is designed to synchronize a chaotic
fractional-order system. To construct a corrective control input, a saturation
function sat(.), with a modified sliding surface is proposed. Finally, Chaos in
the Duffing-Holmes system with fractional orders is investigated, and a
numerical simulation (synchronizing fractional-order Duffing-Holmes _
Duffing-Holmes system) are presented to show the effectiveness of the proposed
controller.Comment: Proc. of the 3rd IFAC Workshop on Fractional Differentiation and its
Applications, Turkey, 200
Modified hybrid combination synchronization of chaotic fractional order systems
The paper investigates a new hybrid synchronization called modified hybrid
synchronization (MHS) via the active control technique. Using the active
control technique, stable controllers which enable the realization of the
coexistence of complete synchronization, anti-synchronization and project
synchronization in four identical fractional order chaotic systems were
derived. Numerical simulations were presented to confirm the effectiveness of
the analytical technique.Comment: 13 pages, 3 postscript figure
Effect of Random Parameter Switching on Commensurate Fractional Order Chaotic Systems
The paper explores the effect of random parameter switching in a fractional
order (FO) unified chaotic system which captures the dynamics of three popular
sub-classes of chaotic systems i.e. Lorenz, Lu and Chen's family of attractors.
The disappearance of chaos in such systems which rapidly switch from one family
to the other has been investigated here for the commensurate FO scenario. Our
simulation study show that a noise-like random variation in the key parameter
of the unified chaotic system along with a gradual decrease in the commensurate
FO is capable of suppressing the chaotic fluctuations much earlier than that
with the fixed parameter one. The chaotic time series produced by such random
parameter switching in nonlinear dynamical systems have been characterized
using the largest Lyapunov exponent (LLE) and Shannon entropy. The effect of
choosing different simulation techniques for random parameter FO switched
chaotic systems have also been explored through two frequency domain and three
time domain methods. Such a noise-like random switching mechanism could be
useful for stabilization and control of chaotic oscillation in many real-world
applications.Comment: 31 pages, 17 figures, 5 Table
Synchronization and secure communication using some chaotic systems of fractional differential equations
Using Caputo fractional derivative of order we
consider some chaotic systems of fractional differential equation. We will
prove that they can be synchronized and anti-synchronized using suitable
nonlinear control function. The synchronized or anti-synchronized error system
of fractional differential equations is used in secure communication.Comment: 10 pages, 6 figure
Reduced order multi switching hybrid synchronization of chaotic systems
In this article, a new synchronization scheme is presented by combining the
concept of reduced-order synchronization with multi-switching synchronization
schemes. The presented scheme, reduced-order multi-switching hybrid
synchronization, is notable addition to the earlier multi-switching schemes
providing enhanced security in applications of secure communication. Based on
the Lyapunov stability theory, the active control method is used to design the
controllers and derive sufficient condition for achieving reduced-order
multi-switching hybrid synchronization between a new hyperchaotic system taken
as drive system and Qi chaotic system serving as response system. Numerical
simulations are performed in MATLAB using the Runge-Kutta method to verify the
effectiveness of the proposed method. The results show the utility and
suitability of the active control method for achieving the reduced-order
multi-switching hybrid synchronization among dynamical chaotic systems.Comment: 16 Pages, 3 figure
Synchronization of piece-wise continuous systems of fractional order
The aim of this study is to prove analytically that synchronization of a
piece-wise continuous class of systems of fractional order can be achieved.
Based on our knowledge, there are no numerical methods to integrate
differential equations with discontinuous right hand side of fractional order
which model these systems. Therefore, via Filippov's regularization [1] and
Cellina's Theorem [2,3], we prove that the initial value problem can be
converted into a continuous problem of fractional-order, to which numerical
methods for fractional orders apply. In this way, the synchronization problem
transforms into a standard problem for continuous systems of fractional order.
Three examples of fractional-order piece-wise systems are considered: Sprott
system, Chen and Shimizu-Morioka system.Comment: Examples revise
Adaptive type-2 fuzzy second order sliding mode control for nonlinear uncertain chaotic system
In this paper, a robust adaptive type-2 fuzzy higher order sliding mode
controller is designed to stabilize the unstable periodic orbits of uncertain
perturbed chaotic system with internal parameter uncertainties and external
disturbances. In Higher Order Sliding Mode Control (HOSMC),the chattering
phenomena of the control effort is reduced, by using Super Twisting algorithm.
Adaptive interval type-2 fuzzy systems are proposed to approximate the unknown
part of uncertain chaotic system and to generate the Super Twisting signals.
Based on Lyapunov criterion, adaptation laws are derived and the closed loop
system stability is guaranteed. An illustrative example is given to demonstrate
the effectiveness of the proposed controller.Comment: 14 pages, 13 figures, International Journal of Computational Science,
Information Technology and Control Engineering (IJCSITCE) Vol.2, No.4,
October 201
Chaotic dynamics of fractional Vallis system for El-Nino
Vallis proposed a simple model for El-Nino weather phenomenon (referred as
Vallis system) by adding an additional parameter p to the Lorenz system. He
showed that the chaotic behavior of the Vallis system is related to the El-Nino
effect. In the present article we study fractional version of Vallis system in
depth. We investigate bifurcations and chaos present in the fractional Vallis
system along with the effect of variation of system parameter p. It is observed
that the range of values of parameter p for which the Vallis system is chaotic,
reduces with the reduction of the fractional order. Further we analyze the
incommensurate fractional Vallis system and find the critical value below which
the system loses chaos. We also synchronize Vallis system with Bhalekar-Gejji
system
Dynamic Sliding Mode Control based on Fractional calculus subject to uncertain delay based chaotic pneumatic robot
This paper considers the chattering problem of sliding mode control while
delay in robot manipulator caused chaos in such electromechanical systems.
Fractional calculus as a powerful theorem to produce a novel sliding mode;
which has a dynamic essence is used for chattering elimination. To realize the
control of a class of chaotic systems in master-slave configuration this novel
fractional dynamic sliding mode control scheme is presented and examined on
delay based chaotic robot in joint and work space. Also the stability of the
closed-loop system is guaranteed by Lyapunov stability theory. Beside these,
delayed robot motions are sorted out for qualitative and quantification study.
Finally, numerical simulation example illustrates the feasibility of proposed
control method.Comment: 8 pages, 9 figures, will be submitted in journa
Different Types of Synchronization in Coupled Network Based Chaotic Circuits
We propose a simple and new unified method to achieve lag, complete and
anticipatory synchronizations in coupled nonlinear systems. It can be
considered as an alternative to the subsystem and intentional parameter
mismatch methods. This novel method is illustrated in a unidirectionally
coupled RC phase shift network based Chua's circuit. Employing feedback
coupling, different types of chaos synchronization are observed experimentally
and numerically in coupled identical chaotic oscillators {\emph{without using
time delay}}. With a simple switch in the experimental set up we observe
different kinds of synchronization. We also analyze the coupled system with
numerical simulations.Comment: 24 pages, 13 figures, Accepted in Communications in Nonlinear Science
and Numerical Simulatio
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