Coexistence behavior of asymmetric attractors in hyperbolic-type memristive Hopfield neural network and its application in image encryption

The neuron model has been widely employed in neural-morphic computing systems and chaotic circuits.This study aims to develop a novel circuit simulation of a three-neuron Hopfield neural network(HNN)with coupled hyperbolic memristors through the modification of a single coupling connection weight.The bistable mode of the hyperbolic memristive HNN(mHNN),characterized by the coexistence of asymmetric chaos and periodic attractors,is effectively demonstrated through the utilization of conventional nonlinear analysis techniques.These techniques include bifurcation diagrams,two-parameter maximum Lyapunov exponent plots,local attractor basins,and phase trajectory diagrams.Moreover,an encryption technique for color images is devised by leveraging the mHNN model and asymmetric structural attractors.This method demonstrates significant benefits in correlation,information entropy,and resistance to differential attacks,providing strong evidence for its effectiveness in encryption.Additionally,an improved modular circuit design method is employed to create the analog equivalent circuit of the memristive HNN.The correctness of the circuit design is confirmed through Multisim simulations,which align with numerical simulations conducted in Matlab.

Delay-dependent Criteria for Robust Stability of Uncertain Switched Hopfield Neural Networks

This paper deals with the problem of delay-dependent robust stability for a class of switched Hopfield neural networks with time-varying structured uncertainties and time-varying delay. Some Lyapunov-KrasoVskii functionals are constructed and the linear matrix inequality （LMI） approach and free weighting matrix method are employed to devise some delay-dependent stability criteria which guarantee the existence, uniqueness and global exponential stability of the equilibrium point for all admissible parametric uncertainties. By using Leibniz-Newton formula, free weighting matrices are employed to express this relationship, which implies that the new criteria are less conservative than existing ones. Some examples suggest that the proposed criteria are effective and are an improvement over previous ones.

ON THE ASYMPTOTIC BEHAVIOR OF HOPFIELD NEURAL NETWORK WITH PERIODIC INPUTS

Without assuming the boundedness and differentiability of the nonlinear activation functions, the new sufficient conditions of the existence and the global exponential stability of periodic solutions for Hopfield neural network with periodic inputs are given by using Mawhin's coincidence degree theory and Liapunov's function method.

A novel chaotic system with one source and two saddle-foci in Hopfield neural networks

This paper presents the finding of a novel chaotic system with one source and two saddle-foci in a simple three-dimensional （3D） autonomous continuous time Hopfield neural network. In particular, the system with one source and two saddle-foci has a chaotic attractor and a periodic attractor with different initial points, which has rarely been reported in 3D autonomous systems. The complex dynamical behaviours of the system are further investigated by means of a Lyapunov exponent spectrum, phase portraits and bifurcation analysis. By virtue of a result of horseshoe theory in dynamical systems, this paper presents rigorous computer-assisted verifications for the existence of a horseshoe in the system for a certain parameter.

Synchronization criteria for coupled Hopfield neural networks with time-varying delays

This paper proposes new delay-dependent synchronization criteria for coupled Hopfield neural networks with time-varying delays. By construction of a suitable Lyapunov Krasovskii＇s functional and use of Finsler＇s lemma, novel synchronization criteria for the networks are established in terms of linear matrix inequalities （LMIs） which can be easily solved by various effective optimization algorithms. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

Existence and Exponential Stability of Almost Periodic Solution for Hopfield Neural Network Equations with Almost Periodic Imput

By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.

Application of Hopfield Neural Networks Approach in Solar Energy Product Conceptual Design

A new product conceptual design approach is put forward based on Hopfield neural networks models. By research on the mechanisms of Hopfield neural networks, the associative simulation approaches are proposed. The approach is given by Hebb learn- ing law, Hopfield neural networks and crossover and mutation. The calculating models and the calculating formulas for the concep- tual design are put forward. Finally, an example for the conceptual design of a solar energy lamp is given. The better results are ob- tained in the conceptual design.

Robust stability for stochastic interval delayed Hopfield neural networks

A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) + WIf(t,u(t)) + WIτf7τ(uτ(t)] dt +σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.

New Delay-dependent Global Asymptotic Stability Condition for Hopfield Neural Networks with Time-varying Delays

This paper deals with the global asymptotic stability problem for Hopfield neural networks with time-varying delays. By resorting to the integral inequality and constructing a Lyapunov-Krasovskii functional, a novel delay-dependent condition is established to guarantee the existence and global asymptotic stability of the unique equilibrium point for a given delayed Hopfield neural network. This criterion is expressed in terms of linear matrix inequalities （LMIs）, which can be easily checked by utilizing the recently developed algorithms for solving LMIs. Examples are provided to demonstrate the effectiveness and reduced conservatism of the proposed condition.

An linear matrix inequality approach to global synchronisation of non-parameter perturbations of multi-delay Hopfield neural network

In this study, a successful linear matrix inequality approach is used to analyse a non-parameter perturbation of multi-delay Hopfield neural network by constructing an appropriate Lyapunov-Krasovskii functional. This paper presents the comprehensive discussion of the approach and also extensive applications.

FPGA implementation and image encryption application of a new PRNG based on a memristive Hopfield neural network with a special activation gradient

A memristive Hopfield neural network(MHNN)with a special activation gradient is proposed by adding a suitable memristor to the Hopfield neural network(HNN)with a special activation gradient.The MHNN is simulated and dynamically analyzed,and implemented on FPGA.Then,a new pseudo-random number generator(PRNG)based on MHNN is proposed.The post-processing unit of the PRNG is composed of nonlinear post-processor and XOR calculator,which effectively ensures the randomness of PRNG.The experiments in this paper comply with the IEEE 754-1985 high precision32-bit floating point standard and are done on the Vivado design tool using a Xilinx XC7 Z020 CLG400-2 FPGA chip and the Verilog-HDL hardware programming language.The random sequence generated by the PRNG proposed in this paper has passed the NIST SP800-22 test suite and security analysis,proving its randomness and high performance.Finally,an image encryption system based on PRNG is proposed and implemented on FPGA,which proves the value of the image encryption system in the field of data encryption connected to the Internet of Things(Io T).

Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique

The global stability problem of Takagi-Sugeno（T-S） fuzzy Hopfield neural networks（FHNNs） with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler＇s lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches.

Filtering and Estimation of Vehicular Dead Reckoning System Based on Hopfield Neural Network

The algorithm of Hopfield neural network filtering and estimation is studied. The model of vehicular dead reckoning system fitting for the algorithm is constructed, and the design scheme of system filtering and estimation based on Hopfield network is proposed. Compared with Kalman filter, the algorithm does not require very precise system model and the prior knowledge of noise statistics and does not diverge easily. The simulation results show that the vehicular dead reckoning system based on Hopfield network filtering and estimation has the good position precision, and needn't require the inertial sensors with high precision. Therefore, the algorithm has the good practicability.

More relaxed condition for dynamics of discrete time delayed Hopfield neural networks

The dynamics of discrete time delayed Hopfield neural networks is investigated. By using a difference inequality combining with the linear matrix inequality, a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found. The result obtained holds not only for constant delay but also for time-varying delays.

PROBE:NOISE-AND-ROTATION RESISTANCE OF HOPFIELD NEURAL NETWORK IN IMAGED TRAFFIC SIGN RECALL

This paper examines the noise and rotation resistance capacity of Hopfield Neural Network (HNN) given four corrupted traffic sign images. In the study, Signal-to-Noise Ratio (SNR), recall rate and pattern complexity are defined and employed to evaluate the recall performance. The experimental results indicate that the HNN possesses significant recall capacity against the strong noise corruption, and certain restoring competence to the rotation. It is also found that combining noise with rotation does not further challenge the HNN corruption resistance capability as the noise or rotation alone does.

Stability of discrete Hopfield neural networks with delay

Discrete Hopfield neural network with delay is an extension of discrete Hopfield neural network. As it is well known, the stability of neural networks is not only the most basic and important problem but also foundation of the network＇s applications. The stability of discrete HJopfield neural networks with delay is mainly investigated by using Lyapunov function. The sufficient conditions for the networks with delay converging towards a limit cycle of length 4 are obtained. Also, some sufficient criteria are given to ensure the networks having neither a stable state nor a limit cycle with length 2. The obtained results here generalize the previous results on stability of discrete Hopfield neural network with delay and without delay.

On-board modeling of gravity fields of elongated asteroids using Hopfield neural networks

To rapidly model the gravity field near elongated asteroids,an intelligent inversion method using Hopfield neural networks(HNNs)is proposed to estimate on-orbit simplified model parameters.First,based on a rotating mass dipole model,the gravitational field of asteroids is characterized using a few parameters.To solve all the parameters of this simplified model,a stepped parameter estimation model is constructed based on different gravity field models.Second,to overcome linearization difficulties caused by the coupling of the parameters to be estimated and the system state,a dynamic parameter linearization technique is proposed such that all terms except the parameter terms are known or available.Moreover,the Lyapunov function of the HNNs is matched to the problem of minimizing parameter estimation errors.Equilibrium values of the Lyapunov function areused as estimated values.The proposed method is applied to natural elongated asteroids 216 Kleopatra,951 Gaspra,and 433 Eros.Simulation results indicate that this method can estimate the simplified model parameters rapidly,and that the estimated simplified model provides a good approximation of the gravity field of elongated asteroids.

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.

Hopfield neural network-based image restoration with adaptive mixed-norm regularization

To overcome the shortcomings of traditional image restoration model and total variation image restoration model, we propose a novel Hopfield neural network-based image restoration algorithm with adaptive mixed-norm regularization. The new error function of image restoration combines the L2-norm and L1- norm regularization types. A method of calculating the adaptive scale control parameter is introduced. Experimental results demonstrate that the proposed algorithm is better than other algorithms with single norm regularization in the improvement of signal-to-noise ratio （ISNR） and vision effect.