Stability Analysis for a Class of Impulsive Bidirectional Associative Memory (BAM) Neural Networks with Distributed Delays and Leakage Time-Varying Delays

Robust Finite-Time Zeroing Neural Networks With Fixed and Varying Parameters for Solving Dynamic Generalized Lyapunov Equation

For solving dynamic generalized Lyapunov equation, two robust finite-time zeroing neural network (RFTZNN) models with stationary and nonstationary parameters are generated through the usage of an improved sign-bi-power (SBP) activation function (AF). Taking differential errors and model implementation errors into account, two corresponding perturbed RFTZNN models are derived to facilitate the analyses of robustness on the two RFTZNN models. Theoretical analysis gives the quantitatively estimated upper bounds for the convergence time (UBs-CT) of the two derived models, implying a superiority of the convergence that varying parameter RFTZNN (VP-RFTZNN) possesses over the fixed parameter RFTZNN (FP-RFTZNN). When the coefficient matrices and perturbation matrices are uniformly bounded, residual error of FP-RFTZNN is bounded, whereas that of VP-RFTZNN monotonically decreases at a super-exponential rate after a finite time, and eventually converges to 0. When these matrices are bounded but not uniform, residual error of FP-RFTZNN is no longer bounded, but that of VP-RFTZNN still converges. These superiorities of VP-RFTZNN are illustrated by abundant comparative experiments, and its application value is further proved by an application to robot.

Sports Video Athlete Detection Based on Associative Memory Neural Network

Aiming at the detection of athletes in sports videos, an automatic detection method based on AMNN is proposed. The background image from the image sequence is obtained, the moving area is extracted, and the color information of pixels to extract the green stadium from the background image is used. In order to improve the accuracy of athletes' detection, the texture similarity measurement method is used to eliminate the shadow in the movement area, the morphological method is used to eliminate the cracks in the area, and the noise outside the stadium is removed according to the stadium information. Combined with the images of nonathletes, a training set is constructed to train the NN classifier. For the input image frames, image pyramids of different scales are constructed by subsampling and the positions of several candidate athletes are detected by NN. The center of gravity of candidate athletes is calculated, a representative candidate athlete is obtained, and then, the final athlete position through a local search process is determined. Experiments show that the system can accurately detect the motion shape of moving targets, can process images in real time, and has good real-time performance.

Impulsive multidirectional associative memory neural networks: New results

An Impulsive Multidirectional Associative Memory Neural Network (IMAMNN) with time-varying and leakage delays is proposed. Through the use of a continuation theorem of coincidence degree theory and differential inequality techniques we establish new conditions for the existence and exponential stability of anti-periodic solutions for the model considered in this work. Moreover, two examples and its numerical simulations are presented to show the validity and the effectiveness of the results.

Bogdanov–Takens Bifurcation in a Neutral Delayed Hopfield Neural Network with Bidirectional Connection

In this paper, a neutral Hopfield neural network with bidirectional connection is considered. In the first step, by choosing the connection weights as parameters bifurcation, the critical point at which a zero root of multiplicity two occurs in the characteristic equation associated with the linearized system. In the second step, we studied the zeros of a third degree exponential polynomial in order to make sure that except the double zero root, all the other roots of the characteristic equation have real parts that are negative. Moreover, we find the critical values to guarantee the existence of the Bogdanov–Takens bifurcation. In the third step, the normal form is obtained and its dynamical behaviors are studied after the use of the reduction on the center manifold and the theory of the normal form. Furthermore, for the demonstration of our results, we have given a numerical example.