Vol. 8, No. 4 (2024): Regular Issue

Many neural networks can be modeled by differential equations. They hold rich dynamics and numerical methods are generally used for numerical simulations. It becomes challenging to determine an appropriate time step--size for long time numerical simulations. This paper suggests a new application of Hopf bifurcation analysis for numerical optimization. First, a discrete--time neural network is obtained by Euler scheme. Then the time step--size is set as a bifurcation parameter and the frequency domain analysis approach is used to determine the critical value. Periodic solutions are obtained by the harmonic balance method. The direction of Hopf bifurcation and sufficient stability conditions are given. Finally, it can be concluded that the method is efficient to find the critical time step--size such that a continuous--time system can be approximated stably.

This paper investigates the issue of chaos-based image encryption. Based on the $z$-shaped fuzzy number, the exponential function, and the modulo operator, a 1-D chaotic map is constructed and studied. This map contains areas with constant chaotic behavior and high Lyapunov exponent values. A statistically secure pseudorandom bit generator is designed based on the new map, and it is used in the encryption process. A three level color image encryption technique is introduced that is based on a shuffling process to the rows and columns of an image, followed by a modulation process in each pixel, and finally by an XOR operation. The resulting ciphertext image is then shown to be resistant to a variety of attacks, including histogram, correlation, and entropy analysis, NPCR and UACI measures, cropping and tampering attacks, and transmission noise. This is demonstrated by applying the encryption to a set of images.

We study the dynamics of identical Leaky Integrate-and-Fire (LIF) neurons on a multiplex composed of two ring networks with symmetric nonlocal coupling within each ring and one-to-one connections between rings. We investigate the impact of different intra-ring coupling strengths in the two rings for attractive and repulsive inter-ring coupling and show that they can lead to subthreshold oscillations. The corresponding parameter spaces where this phenomenon occurs are determined numerically. Moreover, we show that depending on whether the couplings between the two rings are attractive or repulsive, the interaction produces qualitatively different behavior in the synchronization patterns and the mean frequency profiles.

Shock isolation is a critical issue from the point of view of the problem of weapons stored inside submerged platforms from severe underwater shocks. The shock loads may result from the underwater explosion of a nuclear warhead, mines, and bomb nearby submerged platform. These underwater explosions would generate shock loads up to several hundred g's and must protect weapons from severe damage to keep them operational under such circumstances. The most efficient method for reducing shock levels transferred to weapons is shock isolation, which has received little attention from many researchers. Therefore, an Elastic rail shock isolator (ERSI) design was implemented to isolate underwater weapons stored inside submerged platforms to certain acceptable limits. In this study, the prototypes of ERSI were manufactured, and tests were carried out to investigate the isolation effectiveness under laboratory test conditions. The experimental setups were designed, and tests were performed on the universal shock test machine (USTM) equipped with instrumentation to measure the parameters during shock motion, i.e., acceleration and relative displacement of mass. On USTM, a shock input of 170g for 3 ms was characterized, and prototypes were subjected to shock tests to evaluate the performance of ERSI. Finally, the data collected during the shock test was analyzed and compared with analytical results to conclude on isolation performance of ERSI. Thus, the weapon protection was qualified for increasing combat reliability and endurance under attack.

Epilepsy is a highly prevalent neurological disorder worldwide, and the automatic detection of epileptic activity in clinical practice is a significant focus of researchers. In this study, we construct a high-performance model for normal and epileptic electroencephalogram signals using a convolutional neural network architecture called Shallow ConvNet based on the CHB-MIT dataset. The model achieves a maximum classification accuracy of 98%. We also investigate the effects of different data slice and sample sizes on the model performance. Results show that larger data slice sizes can improve accuracy and generalization ability to a certain extent, while increasing the sample size of the training set only improves accuracy but not generalization ability. The best overall performance is achieved by the classifier trained with a slice size of 5 seconds and a training set sample size of 500. These findings provide theoretical guidance for the clinical application of automatic epilepsy detection.

In this paper, a modified Gradient Descent algorithm is investigated, which involves Caputo fractional derivative and a metaheuristic optimizer. Mathematical formulation for convergence analysis of the proposed algorithm is done in this study. Further, this article aims to enhance the initialization for better performance of existing fractional Gradient Descent algorithm. In this study the significance of using fractional derivative in Gradient Descent is also examined. Caputo fractional derivative is preferred due to its memory and non-locality properties. Metaheuristic algorithms are efficient in providing approximate results in fewer iterations. The fractional Gradient Descent algorithm with metaheuristic initialization is given for faster convergence. Further, the fractional Gradient Descent algorithm with a firefly optimizer is applied on the quadratic loss function. Results shows that this hybridization of the firefly optimizer and fractional order Gradient Descent converges in fewer iterations as compared to the existing algorithms.

This study explores the periodic oscillations occurring in a piezoelectric energy harvester exposed to a blend of fluid and harmonic force, with a specific focus on the system’s responses to varying wind velocity. A coupled single degree of freedom model for the electromechanical system is presented. For the external forces, both periodic excitation and aerodynamic galloping are considered. The nonlinear differential equations are discretized, and the expressions of periodic responses are derived through the implicit mapping method. The periodic responses are calculated using the Newton-Raphson method. By assessing the eigenvalues of the resultant matrix derived from the mapping structures, the stabilities and bifurcations of these periodic responses are determined. Furthermore, the study investigates how the displacement and voltage nodes of the energy harvester respond to variations in free stream velocity and excitation amplitude. Maximum eigenvalue magnitudes are also presented for stability assessment. Additionally, utilizing the periodic nodes of displacement and voltage, the harmonic amplitudes are calculated using Fast Fourier Transform, illustrating their variation with changes in free stream velocity. Finally, the study compares implicit maps and numerical simulations for both stable and unstable responses.