Dynamic Analysis, Image Encryption Application and FPGA Implementation of a Discrete Memristor-Coupled Neural Network

Dynamics analysis, FPGA realization and image encryption application of a 5D memristive exponential hyperchaotic system

Numerical simulation of a fractured-vuggy porous medium is a challenging problem. One reason is the coexistence of matrix, fractures and vugs on multiple scales that need to be coupled, and the other reason is that the high-resolution fractured-vuggy model may contain up to several millions of gridcells in applications, which brings severe computational challenges into the numerical methods. Therefore, the requirement for accurate and efficient technique is widely increasing. Fractured-vuggy porous medium is generally represented by triple-continuum model in which the matrix system, fracture system and vug system each are treated as a parallel continuous system. Although triple-continuum model is widely used because of its easy-implementation and high efficiency, it fails to capture the detailed flow patterns of reservoir with disconnected long fractures. Discrete fracture-vug network (DFVN) model can precisely model the fluid flow in fractures and vugs. However, the simulation of this model is deemed intractable even with the advent of supercomputers because of the large amount of calculation. In view of the fact that the multigrid method is now well known as one of the fastest method of solving elliptic problems, in this paper we introduce a nearly linear complexity multiresolution decomposition method for fluid flow in a fractured-vuggy reservoir. The detailed flow patterns are described by combing the advantages of continuum model and discrete model. That is, the homogenization theory is used to construct an equivalent permeability in each coarse grid block in which the vugs and small-scale fractures are represented by discrete fracture-vug network model. We decompose the solution space into several subspaces and then we compute the corresponding solutions of heterogeneous discrete fracture network model in each subspace. Gamblets are constructed and they are elementary solutions of hierarchical information games associated with the process of computing with partial information and limited resources. These gamblets have a natural Bayesian interpretation under the mixed strategy emerging from the game theoretic formulation. This method could realize its fast simulation by decomposing the solution space into a direct sum of linear subspaces that are orthogonal to each other. Finally, the pressure difference distribution of fractured-vuggy porous medium is obtained by combing the DFVN solutions of all subspaces. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed multiresolution decomposition method. The results show that this method is a promising method of numerically simulating the fractured-vuggy porous medium.

In terms of the poor evaluation system of graduation theses, which is easy to be influenced by many human factors, we try to establish a more scientific and objective evaluation model and method of graduation thesis quality. Firstly, the index system of graduation thesis quality evaluation model was constructed, including topic selection, professional knowledge level, data collection capacity, ability to use knowledge, level of guidance teacher, and quality of the paper. Secondly, using expert scoring method, combining Matlab programming and applying AHP, the weight of the quality evaluation elements of graduation thesis was obtained, and the key factors affecting the quality level of graduation thesis were determined. Finally, a discrete Hopfield neural network model for the quality level of graduation thesis was established, and 120 graduation theses were selected for quality level simulation evaluation, and compared with the ideal evaluation results. The results showed that the discrete Hopfield neural network model is correct and it can effectively provide objective, scientific and normative evaluation for the quality of graduation theses. Key words: Undergraduate graduation thesis; AHP; Hopfield; Quality evaluation method

To model the response of neural networks to electromagnetic radiation in real-world environments, this study proposes a memristive dual-wing fractional-order Hopfield neural network (MDW-FOMHNN) model, utilizing a fractional-order memristor to simulate neuronal responses to electromagnetic radiation, thereby achieving complex chaotic dynamics. Analysis reveals that within specific ranges of the coupling strength, the MDW-FOMHNN lacks equilibrium points and exhibits hidden chaotic attractors. Numerical solutions are obtained using the Adomian Decomposition Method (ADM), and the system’s chaotic behavior is confirmed through Lyapunov exponent spectra, bifurcation diagrams, phase portraits, and time series. The study further demonstrates that the coupling strength and fractional order significantly modulate attractor morphologies, revealing diverse attractor structures and their coexistence. The complexity of the MDW-FOMHNN output sequence is quantified using spectral entropy, highlighting the system’s potential for applications in cryptography and related fields. Based on the polynomial form derived from ADM, a field programmable gate array (FPGA) implementation scheme is developed, and the expected chaotic attractors are successfully generated on an oscilloscope, thereby validating the consistency between theoretical analysis and numerical simulations. Finally, to link theory with practice, a simple and efficient MDW-FOMHNN-based encryption/decryption scheme is presented.

This paper proposes an interval discrete wavelet neural network (IDWNN) model with learning algorithm, which can be used for the system modeling with uncertainty. Compared with the conventional interval BP neural network (IBPNN), IDWNN has both the time-frequency localization characteristics of wavelet analysis and the powerful nonlinear approximation ability, which can provide some guidelines for the network structure construction. The algorithms of the forward calculation and the gradient descent-based back propagation training of IDWNN are derived. The numerical simulation results show the advantages of IDWNN in network structure selection and convergence speed.

Using a discrete random network model of the actin cytoskeleton, we studied the effect of stretching of a stiff-fiber on the elastic response of a fibrous network. In real networks, this component can either be a stress-fiber, bundle of fibers within the network, or a microtubule. We analyze the response of this network due to shear loads while the stiff component is under or free of tensile strains. It is observed that the initial response of this network under shear loading is highly dependent on the amount of tensile strain in the stiff-fiber. In addition, the response depends on the amount and the direction of the shear loading, which is either a softening or a stiffening response depending on the loading direction. As a result, the apparent shear modulus of the network containing a preloaded stiff-fiber may become larger or smaller compared to a network with a relaxed stiff-fiber. This effect intensifies for higher levels of tensile strains in the stiff-fiber and for stiffer cross-links, and lessens for higher network densities. The results of the current research are useful in deciphering the response of soft fibrous materials such as the cell cytoskeleton or other networks comprising a random fibrous network containing a stiffer component than the main fibers of the network.

Nonlinear analysis, circuit implementation, and application in image encryption of a four-dimensional multi-scroll hyper-chaotic system

Discrete time-varying matrix problems are prevalent in scientific and engineering fields, and their efficient solution remains a key research objective. Existing direct discrete recurrent neural network models exhibit limitations in noise resistance and are prone to accuracy degradation in complex noise environments. To overcome these deficiencies, this paper proposes a fuzzy integral direct discrete recurrent neural network (FITDRNN) model. The FITDRNN model incorporates an integral term to counteract noise interference and employs a fuzzy logic system for dynamic adjustment of the integral parameter magnitude, thereby further enhancing its noise resistance. Theoretical analysis, combined with numerical experiments and robotic arm trajectory tracking experiments, verifies the convergence and noise resistance of the proposed FITDRNN model.

In this thesis, various artificial recurrent neural network models are investigated for the problem of deriving grammar rules from a finite set of example sentences. A general discrete network framework and its corresponding learning algorithm are presented and studied in detail in learning three different types of grammars. The first type of grammars considered is regular grammars. Experiments with conventional analog recurrent networks in learning regular grammars are presented to demonstrate the unstable behavior of such networks in processing very long strings after training. A new network structure to force recurrent networks to learn stable states by discretizing the internal feedback signals is constructed. For training such discrete networks a learning rule is applied. As an extension to the discrete network model, an external discrete stack is added to accommodate the inference of context-free grammars. A composite error function is devised to deal with various situations during learning. The pseudo-gradient method is also extended to train such a network to learn context-free grammars with the added option of operating on the external stack. Another extension to the discrete network structure is made for the purpose of learning probabilistic finite state grammars. The network consists of a discrete portion which is intended to represent the structure of the grammar, and an analog portion which is intended to represent the transition probabilities. Two criteria for the network to verify the correctness of its solution during training are proposed. Theoretical analysis of the necessary and sufficient conditions for the correct solution is presented. Experimental results show that the discrete network models have similar capabilities in learning various grammars as their analog counterparts, and have the advantage of being provably stable.

Compared with integer order chaotic systems, fractional order chaotic systems can reflect natural phenomena more accurately, which are more suitable for chaotic cryptosystems. In order to explore the application of fractional order chaotic system in cryptography, a novel fractional order hyperchaotic system is constructed and implemented on DSP platform. More progressively, based on Adomian decomposition method, the dynamic behavior is studied by phase diagram, bifurcation diagram, Lyapunov exponent spectrum and spectral entropy (SE) complexity. It is found that each parameter and order have a large range of intervals that can keep the system in a hyperchaotic state. Therefore, the hyperchaotic sequences generated by the constructed fractional order hyperchaotic system have sufficient randomness and are well suited for applications in secure communications. In addition, a color image encryption scheme is designed based on the fractional order hyperchaotic system and DNA dynamic coding. Firstly, the improved Arnold algorithm is used to scramble the original image, then the column cyclic shift method is applied for secondary scrambling, and finally the pixel value is diffused by DNA sequence operation. The security analysis results indicate that the designed encryption algorithm can not only encrypt images effectively, but also has high security and can resist various common attacks.

Design and realization of discrete memristive hyperchaotic map with application in image encryption

Image privacy is getting more and more attention, so it is necessary to design a secure and efficient image encryption algorithm. This paper proposes a novel Logistics-Henon-Memristor Coupled Chaotic Map (LHM-CCM), which exhibits high sensitivity to system parameters as demonstrated by Lyapunov exponents, bifurcation diagrams, offset-boosting analysis and extreme multistability. Based on this system, a non-uniform pixel segmentation image encryption algorithm with multiple randomization elements is introduced, dynamically controlling pixel segmentation using a hash matrix. The Josephus scrambling and bit-plane reconstruction achieve disruption and diffusion, respectively. It shows excellent performance in terms of sequence randomness, resistance to attacks, key security, and robustness against interference. Moreover, encrypting a 256 × 256 grayscale image only takes 0.0696 s. The proposed algorithm demonstrates significant advantages in encryption and decryption efficiency while ensuring security.

Stability and bifurcation of a two-dimension discrete neural network model with multi-delays

The planning, regulation and effectiveness of the product design process depend on various characteristics. Recently, bio-inspired collective intelligence approaches have been applied in this process in order to create more appealing product forms and optimize the design process. In fact, the use of neural network models in product form design analysis is a complex process, in which the type of network has to be determined, as well as the structure of the network layers and the neurons in them; the connection coefficients, inputs and outputs have to be explored; and the data have to be collected. In this paper, an impulsive discrete fractional neural network modeling approach is introduced for product design analysis. The proposed model extends and complements several existing integer-order neural network models to the generalized impulsive discrete fractional-order setting, which is a more flexible mechanism to study product form design. Since control and stability methods are fundamental in the construction and practical significance of a neural network model, appropriate impulsive controllers are designed, and practical Mittag-Leffler stability criteria are proposed. The Lyapunov function strategy is applied in providing the stability criteria and their efficiency is demonstrated via examples and a discussion. The established examples also illustrate the role of impulsive controllers in stabilizing the behavior of the neuronal states. The proposed modeling approach and the stability results are applicable to numerous industrial design tasks in which multi-agent systems are implemented.

This paper puts forward a novel image encryption algorithm that is based on permutation-diffusion architecture. In pixels' permutation stage, algorithm takes full advantage of the idea of magic cube's scrambling. There is only simple cyclic shift operation in each sub-block's permutation, but when the algorithm has disposed the current sub-block, the adjacent sub-blocks will be dealt with, too. In the cyclic shift of each row, stable points will help to decrease the correlation of adjacent pixels. To make encryption procedure uncertain, this paper brings in a parameter named delay-time that is generated by chaotic map. In the diffusion stage, by combining multiple operations and dynamic look-up table together, the proposed algorithm highly increases the uncertainty of the encryption procedure. At last, the experiment results of key space analysis, information entropy analysis, histogram analysis and etc. show that the encryption algorithm has well performance and it can be used in image encryption and transmission.