No abstract is provided for this article.
No abstract is provided for this article.
It is generally difficult to synchronize a ring network that features single nearest-neighbor coupling, if the number N of nodes of the network is too large. In this paper, we consider a ring network of N identical nodes, which are unidirectionally coupled through the first state variable of each node. We present a new nonlinear integral method for synchronization of such a network, and derive a sufficient condition for synchronization of this type of network with chaotic nodes. The entire ring network will synchronize by adding only one nonlinear integral feedback, even if the feedback gain is very small. As examples, we study the synchronization of such a network with Lorenz system nodes and Chua’s system nodes. Our numerical simulations confirm the effectiveness of the new method.
No abstract is provided for this article.
This Letter considers the robust adaptive tracking control problem of a class of uncertain chaotic systems with time-varying unknown but bounded parameters. A novel controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic systems globally asymptotically track the desired bounded trajectories. Simulation results verify the effectiveness of the proposed controller.
In this paper, a simple feedback control design method earlier proposed by us for discrete-time dynamical systems is proved to be a mathematically rigorous approach for anticontrol of chaos, in the sense that any given discrete-time dynamical system can be made chaotic by the designed state-feedback controller along with the mod-operations.
The traveling wave system of a microstructured solid model belongs to the second class of singular traveling wave equations studied in [Li et al., 2009]. In this paper, by using methods from dynamical systems theory, bifurcations of phase portraits of such a traveling wave system are analyzed in its corresponding parameter space. The existence of kink wave solutions and uncountably infinitely many bounded solutions is proved. Moreover, the exact parametric representations of periodic solutions and homoclinic orbits are obtained.
In this paper, two kinds of chaotic coupling synchronization schemes are presented. The synchronizability of the coupled hyperchaotic oscillators is proved mathematically and the numerical simulation is also carried out. The numerical calculation of the largest conditional Lyapunov exponent shows that in a given range of coupling strengths, chaotic-coupling synchronization is quicker than the typical continuous-coupling synchronization.
In this paper, a chaos-based watermarking algorithm is developed in the wavelet domain for still images. The wavelet transform is commonly applied for watermarking, where the whole image is transformed in the frequency domain. In contrast to this conventional approach, we apply the wavelet transform only locally. We transform the subimage, which is extracted from the original image, in the frequency domain by using DWT and then embed the chaotic watermark into part of the subband coefficients. As usual, the watermark is detected by computing the correlation between the watermarked coefficients and the watermarking signal, where the watermarking threshold is chosen according to the Neyman–Pearson criterion based on some statistical assumptions. Watermark detection is accomplished without using the original image. Simulation results show that we can gain high fidelity and high robustness, especially under the typical attack of geometric operations.