Periodic solution and chaotic strange attractor for shunting inhibitory cellular neural networks with impulses

Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument

In the paper, shunting inhibitory cellular neural networks with impulses and the generalized piecewise constant argument are under discussion. The main modeling novelty is that the impulsive part of the systems is symmetrical to the differential part. Moreover, the model depends not only on the continuous time, but also the generalized piecewise constant argument. The process is subdued to Poisson stable inputs, which cause the new type of recurrent signals. The method of included intervals, recently introduced approach of recurrent motions checking, is effectively utilized. The existence and asymptotic properties of the unique Poisson stable motion are investigated. Simulation examples for results are provided. Finally, comparing impulsive shunting inhibitory cellular neural networks with former neural network models, we discuss the significance of the components of our model.

Design and implementation of EP-based PID controller for chaos synchronization of Rikitake circuit systems

This article addresses an evolutionary programming (EP) algorithm technique-based and proportional-integral-derivative (PID) control methods are established to guarantee synchronization of the master and slave Rikitake chaotic systems. For PID synchronous control, the evolutionary programming (EP) algorithm is used to find the optimal PID controller parameters k_p, k_i, k_d by integrated absolute error (IAE) method for the convergence conditions. In order to verify the system performance, the basic electronic components containing operational amplifiers (OPAs), resistors, and capacitors are used to implement the proposed chaotic Rikitake systems. Finally, the experimental results validate the proposed Rikitake chaotic synchronization approach.

Chaotifying delayed recurrent neural networks via impulsive effects

In this paper, chaotification of delayed recurrent neural networks via chaotically changing moments of impulsive actions is considered. Sufficient conditions for the presence of Li-Yorke chaos with its ingredients proximality, frequent separation, and existence of infinitely many periodic solutions are theoretically proved. Finally, effectiveness of our theoretical results is illustrated by an example with numerical simulations.

Shunting inhibitory cellular neural networks with chaotic external inputs

Taking advantage of external inputs, it is shown that shunting inhibitory cellular neural networks behave chaotically. The analysis is based on the Li-Yorke definition of chaos. Appropriate illustrations which support the theoretical results are depicted.

Stationary oscillation for chaotic shunting inhibitory cellular neural networks with impulses

In this paper, we study stationary oscillation for general shunting inhibitory cellular neural networks with impulses which are complex nonlinear neural networks. In a recent paper [Z. J. Gui and W. G. Ge, Chaos 16, 033116 (2006)], the authors claimed that they obtained a criterion of existence, uniqueness, and global exponential stability of periodic solution (i.e., stationary oscillation) for shunting inhibitory cellular neural networks with impulses. We point out in this paper that the main result of their paper is incorrect, and presents a sufficient condition of ensuring existence, uniqueness, and global stability of periodic solution for general shunting inhibitory cellular neural networks with impulses. The result is derived by using a new method which is different from those of previous literature. An illustrative example is given to demonstrate the effectiveness.

Optimizing chaos-based signals for complex radar targets

There has been interest in the use of chaotic signals for radar, but most researchers consider only a few chaotic systems and how these signals perform for the detection of point targets. The range of possible chaotic signals is far greater than what most of these researchers consider, so to demonstrate this, I use a chaotic map whose parameters may be adjusted by a numerical optimization routine, producing different chaotic signals that are modulated onto a carrier and optimized for different situations. It is also suggested that any advantage for these chaos-based signals may come in the detection of complex targets, not point targets, and I compare the performance of chaos-based signals to a standard radar signal, the linear frequency modulated chirp. I find that I can optimize a chaos-based signal to increase the cross-correlation with the reflection from one complex target compared to the cross-correlation with the reflection from a different target, thus allowing the identification of a complex target. I am also able to increase the cross-correlation of the reflection from a complex target compared with the cross-correlation with the reflection from spatially extended clutter. I show that a larger output signal-to-noise ratio is possible if I cross-correlate with a reference signal that is different from the transmitted signal, and I justify my results by showing how the ambiguity diagram for a chaos-based signal can be different than the ambiguity diagram for a noise signal.

Stability analysis of neural networks with interval time-varying delays

The global exponential stability is investigated for neural networks with interval time-varying delays. Based on the Leibniz-Newton formula and linear matrix inequality technique, delay-dependent stability criteria are proposed to guarantee the exponential stability of neural networks with interval time-varying delays. Some numerical examples and comparisons are provided to show that the proposed results significantly improve the allowable upper and lower bounds of delays over some existing ones in the literature.