Abstract: This paper addresses functional projective lag synchronization of Lorenz system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. For this purpose, an adaptive control law is proposed to make the states of two identical Lorenz systems asymptotically synchronize up. Based on Lyapunov stability theory, a novel criterion is given for asymptotical stability of the null solution of an error dynamics. Finally, some numerical examples are provided to show the effectiveness of our results.
Abstract: In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. The VIM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the considered model and other dynamical systems. We shall call this technique as the piecewise VIM. Numerical comparisons between the piecewise VIM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the proposed technique is a promising tool for the nonlinear chaotic and nonchaotic systems.
Abstract: This paper presents a novel control method based on radial basis function networks (RBFNs) for chaotic dynamical systems. The proposed method first identifies the nonlinear part of the chaotic system off-line and then constructs a model-following controller using only the estimated system parameters. Simulation results show the effectiveness of the proposed control scheme.
Abstract: In this paper, a generalized synchronization scheme, which is called function synchronization, for chaotic systems is studied. Based on Lyapunov method and active control method, we design the synchronization controller for the system such that the error dynamics between master and slave chaotic systems is asymptotically stable. For verification of our theory, computer and circuit simulations for a specific chaotic system is conducted.
Abstract: In this paper, we present a robust and secure
algorithm for watermarking, the watermark is first transformed into
the frequency domain using the discrete wavelet transform (DWT).
Then the entire DWT coefficient except the LL (Band) discarded,
these coefficients are permuted and encrypted by specific mixing.
The encrypted coefficients are inserted into the most significant
spectral components of the stego-image using a chaotic system. This
technique makes our watermark non-vulnerable to the attack (like
compression, and geometric distortion) of an active intruder, or due
to noise in the transmission link.
Abstract: Chua’s circuit is one of the most important electronic devices that are used for Chaos and Bifurcation studies. A central role of secure communication is devoted to it. Since the adaptive control is used vastly in the linear systems control, here we introduce a new trend of application of adaptive method in the chaos controlling field. In this paper, we try to derive a new adaptive control scheme for Chua’s circuit controlling because control of chaos is often very important in practical operations. The novelty of this approach is for sake of its robustness against the external perturbations which is simulated as an additive noise in all measured states and can be generalized to other chaotic systems. Our approach is based on Lyapunov analysis and the adaptation law is considered for the feedback gain. Because of this, we have named it NAFT (Nonlinear Adaptive Feedback Technique). At last, simulations show the capability of the presented technique for Chua’s circuit.
Abstract: In this paper, stability and Hopf bifurcation analysis of
a novel hyperchaotic system are investigated. Four feedback control
strategies, the linear feedback control method, enhancing feedback
control method, speed feedback control method and delayed feedback
control method, are used to control the hyperchaotic attractor to
unstable equilibrium. Moreover numerical simulations are given to
verify the theoretical results.
Abstract: This paper at first presents approximate analytical
solutions for systems of fractional differential equations using the
differential transform method. The application of differential
transform method, developed for differential equations of integer
order, is extended to derive approximate analytical solutions of
systems of fractional differential equations. The solutions of our
model equations are calculated in the form of convergent series with
easily computable components. After that a drive-response
synchronization method with linear output error feedback is
presented for “generalized projective synchronization" for a class of
fractional-order chaotic systems via a scalar transmitted signal.
Genesio_Tesi and Duffing systems are used to illustrate the
effectiveness of the proposed synchronization method.
Abstract: In this paper, a fuzzy controller is designed for
stabilization of the Lorenz chaotic equations. A simple Mamdani
inference method is used for this purpose. This method is very simple
and applicable for complex chaotic systems and it can be
implemented easily. The stability of close loop system is investigated
by the Lyapunov stabilization criterion. A Lyapunov function is
introduced and the global stability is proven. Finally, the
effectiveness of this method is illustrated by simulation results and it
is shown that the performance of the system is improved.
Abstract: The majority of existing predictors for time series are
model-dependent and therefore require some prior knowledge for the
identification of complex systems, usually involving system
identification, extensive training, or online adaptation in the case of
time-varying systems. Additionally, since a time series is usually
generated by complex processes such as the stock market or other
chaotic systems, identification, modeling or the online updating of
parameters can be problematic. In this paper a model-free predictor
(MFP) for a time series produced by an unknown nonlinear system or
process is derived using tracking theory. An identical derivation of the
MFP using the property of the Newton form of the interpolating
polynomial is also presented. The MFP is able to accurately predict
future values of a time series, is stable, has few tuning parameters and
is desirable for engineering applications due to its simplicity, fast
prediction speed and extremely low computational load. The
performance of the proposed MFP is demonstrated using the
prediction of the Dow Jones Industrial Average stock index.