Dynamic analysis and application in medical digital image watermarking of a new multi-scroll neural network with quartic nonlinear memristor

A novel 4D chaotic system coupling with dual-memristors and application in image encryption

A novel 4D dual-memristor chaotic system (4D-DMCS) is constructed by concurrently introducing two types of memristors: an ideal quadratic smooth memristor and a memristor with an absolute term, into a newly designed jerk chaotic system. The excellent nonlinear properties of the system are investigated by analyzing the Lyapunov exponent spectrum, and bifurcation diagram. The 4D-DMCS retains some characteristics of the original jerk chaotic system, such as the offset boosting in the x-axis direction. Simultaneously, the integration of the two memristors significantly enriches the dynamic behavior of the system, notably augmenting its transitional behaviors, fostering greater multistability, and elevating both spectral entropy and C0 complexity. This augmentation underscores the profound impact of the memristors on the system's overall performance and complexity. The system is implemented through the STM32 microcontroller, further proving the physical realizability of the system. Ultimately, the 4D-DMCS exhibits remarkable performance when applied to image encryption, demonstrating its significant potential and effectiveness in this domain.

Artificial synapses based on HfOx/TiOymemristor devices for neuromorphic applications

As a result of enormous progress in nanoscale electronics, interest in artificial intelligence (AI) supported systems has also increased greatly. These systems are typically designed to process computationally intensive data. Parallel processing neural network architectures are particularly noteworthy for their ability to process dense data at high speeds, making them suitable candidates for AI algorithms. Due to their ability to combine processing and memory functions in a single device, memristors offer a significant advantage over other electronic platforms in terms of area scaling efficiency and energy savings. In this study, single-layer and bilayer metal-oxide HfOxand TiOymemristor devices inspired by biological synapses were fabricated by pulsed laser and magnetron sputtering deposition techniques in high vacuum with different oxide thicknesses. The structural and electrical properties of the fabricated devices were analysed using x-ray reflectivity, x-ray photoelectron spectroscopy, and standard two-probe electrical characterization measurements. The stoichiometry and degree of oxidation of the elements in the oxide material for each thin film were determined. Moreover, the switching characteristics of the metal oxide upper layer in bilayer devices indicated its potential as a selective layer for synapse. The devices successfully maintained the previous conductivity values, and the conductivity increased after each pulse and reached its maximum value. Furthermore, the study successfully observed synaptic behaviours with long-term potentiation, long-term depression (LTD), paired-pulse facilitation, and spike-timing-dependent plasticity, showcasing potential of the devices for neuromorphic computing applications.

Dynamic Analysis and FPGA Implementation of a New Fractional-Order Hopfield Neural Network System under Electromagnetic Radiation

Fractional calculus research indicates that, within the field of neural networks, fractional-order systems more accurately simulate the temporal memory effects present in the human brain. Therefore, it is worthwhile to conduct an in-depth investigation into the complex dynamics of fractional-order neural networks compared to integer-order models. In this paper, we propose a magnetically controlled, memristor-based, fractional-order chaotic system under electromagnetic radiation, utilizing the Hopfield neural network (HNN) model with four neurons as the foundation. The proposed system is solved by using the Adomain decomposition method (ADM). Then, through dynamic simulations of the internal parameters of the system, rich dynamic behaviors are found, such as chaos, quasiperiodicity, direction-controllable multi-scroll, and the emergence of analogous symmetric dynamic behaviors in the system as the radiation parameters are altered, with the order remaining constant. Finally, we implement the proposed new fractional-order HNN system on a field-programmable gate array (FPGA). The experimental results show the feasibility of the theoretical analysis.

Star Memristive Neural Network: Dynamics Analysis, Circuit Implementation, and Application in a Color Cryptosystem

At present, memristive neural networks with various topological structures have been widely studied. However, the memristive neural network with a star structure has not been investigated yet. In order to investigate the dynamic characteristics of neural networks with a star structure, a star memristive neural network (SMNN) model is proposed in this paper. Firstly, an SMNN model is proposed based on a Hopfield neural network and a flux-controlled memristor. Then, its chaotic dynamics are analyzed by using numerical analysis methods including bifurcation diagrams, Lyapunov exponents, phase plots, Poincaré maps, and basins of attraction. The results show that the SMNN can generate complex dynamical behaviors such as chaos, multi-scroll attractors, and initial boosting behavior. The number of multi-scroll attractors can be changed by adjusting the memristor's control parameters. And the position of the coexisting chaotic attractors can be changed by switching the memristor's initial values. Meanwhile, the analog circuit of the SMNN is designed and implemented. The theoretical and numerical results are verified through MULTISIM simulation results. Finally, a color image encryption scheme is designed based on the SMNN. Security performance analysis shows that the designed cryptosystem has good security.

Four-scroll attractor on the dynamics of a novel Hopfield neural network based on bi-neurons without bias current

The dynamics of a neural network under several factors (bias current and electromagnetic induction effect) are recently used to simulate activities of the brain under different excitation. In this paper, we introduce a novel Hopfield neural network (HNN) based on two neurons with a memristive synaptic weight connected between neuron one and two based of flux controlled memristor recently proposed by Hua M. et al., in 2022. Using analysis tools, we proved that this model can develop rich dynamical characteristics such as various number of equilibrium points when the parameters are varied, four-scroll attractors, transient chaos, multistability of more than three different attractors and intermittency chaos phenomenon are reported. Moreover, when increasing a synaptic weight, the model shows bursting oscillations phenomenon. To obtain the normal state of the brain, the control of multistability to a strange monostable state is carry out. Finally, microcontroller implementation of the model is considered to verify the numerical analysis.

A novel activation function based recurrent neural networks and their applications on sentiment classification and dynamic problems solving

In this paper, a nonlinear activation function (NAF) is proposed to constructed three recurrent neural network (RNN) models (Simple RNN (SRNN) model, Long Short-term Memory (LSTM) model and Gated Recurrent Unit (GRU) model) for sentiment classification. The Internet Movie Database (IMDB) sentiment classification experiment results demonstrate that the three RNN models using the NAF achieve better accuracy and lower loss values compared with other commonly used activation functions (AF), such as ReLU, SELU etc. Moreover, in terms of dynamic problems solving, a fixed-time convergent recurrent neural network (FTCRNN) model with the NAF is constructed. Additionally, the fixed-time convergence property of the FTCRNN model is strictly validated and the upper bound convergence time formula of the FTCRNN model is obtained. Furthermore, the numerical simulation results of dynamic Sylvester equation (DSE) solving using the FTCRNN model indicate that the neural state solutions of the FTCRNN model quickly converge to the theoretical solutions of DSE problems whether there are noises or not. Ultimately, the FTCRNN model is also utilized to realize trajectory tracking of robot manipulator and electric circuit currents computation for the further validation of its accurateness and robustness, and the corresponding results further validate its superior performance and widespread applicability.

Dynamics study on the effect of memristive autapse distribution on Hopfield neural network

As the shortest feedback loop of the nervous system, autapse plays an important role in the mode conversion of neurodynamics. In particular, memristive autapses can not only facilitate the adjustment of the dynamical behavior but also enhance the complexity of the nervous system, in view of the fact that the dynamics of the Hopfield neural network has not been investigated and studied in detail from the perspective of memristive autapse. Based on the traditional Hopfield neural network, this paper uses a locally active memristor to replace the ordinary resistive autapse so as to construct a 2 n-dimensional memristive autaptic Hopfield neural network model. The boundedness of the model is proved by introducing the Lyapunov function and the stability of the equilibrium point is analyzed by deriving the Jacobian matrix. In addition, four scenarios are established on a small Hopfield neural network with three neurons, and the influence of the distribution of memristive autapses on the dynamics of this small Hopfield neural network is described by numerical simulation tools. Finally, the Hopfield neural network model in these four situations is designed and implemented on field-programmable gate array by using the fourth-order Runge-Kutta method, which effectively verifies the numerical simulation results.

Asymptotic Synchronization of Memristive Cohen-Grossberg Neural Networks with Time-Varying Delays via Event-Triggered Control Scheme

This paper investigates the asymptotic synchronization of memristive Cohen-Grossberg neural networks (MCGNNs) with time-varying delays under event-triggered control (ETC). First, based on the designed feedback controller, some ETC conditions are provided. It is demonstrated that ETC can significantly reduce the update times of the controller and decrease the computing cost. Next, some sufficient conditions are derived to ensure the asymptotic synchronization of MCGNNs with time-varying delays under the ETC method. Finally, a numerical example is provided to verify the correctness and effectiveness of the obtained results.