Discrete Neural Network Model Research Articles

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

This paper presents a novel discrete memristor model that incorporates exponential and absolute value functions. A discrete coupled memristor neural network model is constructed based on this memristor design. The periodic and chaotic regions of the discrete neural network model are determined using bifurcation and Lyapunov exponent spectrum. Furthermore, by varying the initial values of the discrete memristive neural network, we observe the coexistence of chaos and periodic attractors, as well as periodic attractors. Additionally, an application to color image encryption based on the discrete system model is given. Security analysis is conducted in the aspects of key space, histogram analysis, correlation analysis, sensitivity analysis, Peak Signal-to-Noise Ratio (PSNR), and information entropy analysis. The analysis results show that the algorithm has a key space size of [Formula: see text], and the information entropy of baboon graph is 7.9993, which is very close to the ideal value of 8. It shows that the image encryption algorithm is feasible and effective. Finally, the implementation of the discrete memristive neural network model is realized using Field Programmable Gate Array (FPGA). The experimental implementation is conducted using the Verilog language on the Vivado 2018.3 platform, and the obtained results align with the numerical simulation results obtained through MATLAB.

Mean-squared exponential stability of distributed almost periodic sequence for nonlocal space-time discrete shunting inhibitory cellular neural networks with Brownian motions

The discrete-time and discrete-space model for stochastic nonlocal shunting inhibitory cellular neural networks with reaction diffusions are modelled in the first time. Owing to the consideration of spatial variables, the discrete model derived in this article is more complex than the traditional ordinary difference model. In accordance with the constant-variation-formula for discrete-time and discrete-space model, Banach contracting mapping principle, the method of proof by contradiction and stochastic calculus, we also obtain the existence of a unique bounded almost periodic sequence for the discrete model, which is exponentially stable in the mean-square sense. Noting that it is the first time to consider the dynamics of almost periodicity in distribution of time-space discrete neural network models. The practicability of the present results is demonstrated by means of an illustration.

Nonlinear dynamics of a three-dimensional discrete-time delay neural network

This paper examines a three-dimensional delayed discrete neural network model analytically and numerically to determine the existence of different types of bifurcations of the involved fixed points. The model exhibits different bifurcations such as pitchforks, flips, Neimark–Sackers, and flip-Neimark–Sackers. The critical coefficients are used to determine the structure of each bifurcation. The curves are calculated and plotted for each bifurcation when the parameters are changed. Further, these bifurcations are theoretically analyzed and numerically verified. From the obtained results, we observed that by drawing the curves associated with each bifurcation, the numerical simulations are consistent with the analytical results.

Bifurcations and complex dynamics of a two dimensional neural network model with delayed discrete time

This paper focuses on the different bifurcations of fixed points of a delayed discrete neural network model analytically and numerically. The conditions and critical values of different bifurcations including the pitchfork, flip, Neimark–Sacker, and flip–Neimark–Sacker are analyzed. By using the critical coefficients, the structure for each bifurcation are determined. By taking one and two parameters, the critical coefficients are calculated and the curves associated with each bifurcation are plotted. The numerical simulation results demonstrate the effectiveness and feasibility of the proposed method.

Discrete memristor applied to construct neural networks with homogeneous and heterogeneous coexisting attractors

Memristors are widely used to simulate the effects of electromagnetic radiation on neurons or as synapses to simulate excitation and inhibition between neurons. This paper constructs discrete neural network models (DNNMs) in three scenarios: without discrete memristor, discrete memristor simulate electromagnetic radiation stimulation, and discrete local active memristor simulate synapses. Research reveals that the DNNM without fixed points under electromagnetic radiation stimulation, which in turn induces hidden hyperchaotic attractors and also observes the existence of infinite coexisting homogeneous attractors. Meanwhile, the DNNM can generate heterogeneous coexisting attractors after introducing a memristor to mimic synapses. Numerical results show that discrete memristors can induce the DNNM to develop more complex chaotic dynamics. In addition, a hardware platform is designed to validate the numerical results, and the DNNMs are applied to construct the pseudo-random number generator (PRNG).

The new fractional discrete neural network model under electromagnetic radiation: Chaos, control and synchronization

This paper describes a new four-dimensional fractional discrete neural network with electromagnetic radiation model. In addition, the non-linear dynamics of the suggested model are examined, within the framework of commensurate, incommensurate and variable orders, through different numerical techniques such as Lyapunov exponent, phase portraits, bifurcation diagrams, and the 0–1 test method. The results imply that The behaviours of the proposed fractional discrete neural network model have rich and complex dynamical properties that are influenced by the variation of the system parameters, the commensurate order, the incommensurate order and the variable order. Moreover, the approximate entropy test and Co algorithm are carried out to measure complexity and validate the presence of chaos. Finally, nonlinear controllers are illustrated to stabilize and synchronize the proposed model.

Dynamic Behavior Analysis and Synchronization of Memristor-Coupled Heterogeneous Discrete Neural Networks

Continuous memristors have been widely studied in recent years; however, there are few studies on discrete memristors in the field of neural networks. In this paper, a four-stable locally active discrete memristor (LADM) is proposed as a synapse, which is used to connect a two-dimensional Chialvo neuron and a three-dimensional KTZ neuron, and construct a simple heterogeneous discrete neural network (HDNN). Through a bifurcation diagram and Lyapunov exponents diagram, the period and chaotic regions of the discrete neural network model are shown. Through numerical analysis, it was found that the chaotic region and periodic region of the neural network based on DLAM are significantly improved. In addition, coexisting chaos and chaos attractors, coexisting periodic and chaotic attractors, and coexisting periodic and periodic attractors will appear when the initial value of the LADM is changed. Coupled by a LADM synapse, two heterogeneous discrete neurons are gradually synchronized by changing the coupling strength. This paper lays a good foundation for the future analysis of LADMs and the related research of discrete neural networks coupled by LADMs.

On Variable-Order Fractional Discrete Neural Networks: Solvability and Stability

Few papers have been published to date regarding the stability of neural networks described by fractional difference operators. This paper makes a contribution to the topic by presenting a variable-order fractional discrete neural network model and by proving its Ulam–Hyers stability. In particular, two novel theorems are illustrated, one regarding the existence of the solution for the proposed variable-order network and the other regarding its Ulam–Hyers stability. Finally, numerical simulations of three-dimensional and two-dimensional variable-order fractional neural networks were carried out to highlight the effectiveness of the conceived theoretical approach.

Neural Networks in Engineering Design: Robust Practical Stability Analysis

Abstract In recent years, we are witnessing artificial intelligence being deployed on embedded platforms in our everyday life, including engineering design practice problems starting from early stage design ideas to the final decision. One of the most challenging problems is related to the design and implementation of neural networks in engineering design tasks. The successful design and practical applications of neural network models depend on their qualitative properties. Elaborating efficient stability is known to be of a high importance. Also, different stability notions are applied for differently behaving models. In addition, uncertainties are ubiquitous in neural network systems, and may result in performance degradation, hazards or system damage. Driven by practical needs and theoretical challenges, the rigorous handling of uncertainties in the neural network design stage is an essential research topic. In this research, the concept of robust practical stability is introduced for generalized discrete neural network models under uncertainties applied in engineering design. A robust practical stability analysis is offered using the Lyapunov function method. Since practical stability concept is more appropriate for engineering applications, the obtained results can be of a practical significance to numerous engineering design problems of diverse interest.

Three cell symmetry discrete-time-delayed neural network

In this paper, we consider several three-dimension discrete neural network models representing the models containing symmetry with time-delayed connections. The existence of symmetric property is investigated. We examine the relation between the structure of a discrete network and the spatio-temporally symmetric periodic dynamics it can support. We illustrate the existence of spatio-temporally periodic solutions through a direct construction of symmetric groups, and show that these solutions can be stable in some region of parameter space. We give computer simulations to support the theoretical predictions.

Symmetry discrete-time delayed neural network

In this paper, we consider a three-dimensional discrete neural network model with delay. The characteristic equation of the linearized system at the zero solution is a polynomial equation involving very high order terms. We derive some sufficient and necessary conditions on the asymptotic stability and multiple bifurcations of the zero solution. We give computer simulations to support the theoretical predictions.

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

Abstract A two-dimension discrete neural network model with multi-delays is obtained using Euler method. Furthermore, the linear stability of the model is studied. It is found that there exists Hopf bifurcations when the delay passes a sequence of critical values. Using the normal form method and the center manifold theorem, the explicit formulas which determine the direction of the Hopf bifurcations and the stability of bifurcating periodic solutions are derived. Finally, computer simulations are performed to support the theoretical predictions.

Hopf bifurcation in numerical approximation of a n-dimension neural network model with multi-delays

Abstract In this paper we consider the numerical approximation of a n -dimension neural network model with multi-delays undergoing a Hopf bifurcation. We prove that if the neural network model has a Hopf bifurcation point at τ = τ ∗ , then the discrete neural network model obtained by Euler-method also has a Hopf bifurcation point at τ h = τ ∗ + O ( h ).

A note on the complexity of reliability in neural networks

It is shown that in a standard discrete neural network model with small fan-in, tolerance to random malicious faults can be achieved with a log-linear increase in the number of neurons and a constant factor increase in parallel time, provided fan-in can increase arbitrarily. A similar result is obtained for a nonstandard but closely related model with no restriction on fan-in.