本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Ra...本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Rassias稳定性的一个充分条件,从而提供了一种通过验证自反馈系数矩阵和权重系数矩阵判断神经网络具有Hyers-Ulam稳定性的方法.最后,本文设置满足定理的神经网络系数,利用仿真实验,验证此充分条件的正确性.展开更多
The large-scale acquisition and widespread application of remote sensing image data have led to increasingly severe challenges in information security and privacy protection during transmission and storage.Urban remot...The large-scale acquisition and widespread application of remote sensing image data have led to increasingly severe challenges in information security and privacy protection during transmission and storage.Urban remote sensing image,characterized by complex content and well-defined structures,are particularly vulnerable to malicious attacks and information leakage.To address this issue,the author proposes an encryption method based on the enhanced single-neuron dynamical system(ESNDS).ESNDS generates highquality pseudo-random sequences with complex dynamics and intense sensitivity to initial conditions,which drive a structure of multi-stage cipher comprising permutation,ring-wise diffusion,and mask perturbation.Using representative GF-2 Panchromatic and Multispectral Scanner(PMS)urban scenes,the author conducts systematic evaluations in terms of inter-pixel correlation,information entropy,histogram uniformity,and number of pixel change rate(NPCR)/unified average changing intensity(UACI).The results demonstrate that the proposed scheme effectively resists statistical analysis,differential attacks,and known-plaintext attacks while maintaining competitive computational efficiency for high-resolution urban image.In addition,the cipher is lightweight and hardware-friendly,integrates readily with on-board and ground processing,and thus offers tangible engineering utility for real-time,large-volume remote-sensing data protection.展开更多
Neural synchronization is associated with various brain disorders,making it essential to investigate the intrinsic factors that influence the synchronization of coupled neural networks.In this paper,we propose a minim...Neural synchronization is associated with various brain disorders,making it essential to investigate the intrinsic factors that influence the synchronization of coupled neural networks.In this paper,we propose a minimal architecture as a prototype,consisting of two bi-neuron Hopfield neural networks(HNNs)coupled via a memristor.This coupling elevates the original two bi-neuron HNNs into a five-dimensional system,featuring an unstable line equilibrium set and rich dynamics absent in the uncoupled case.Our results show that varying the coupling strength and the initial state of the memristor can induce periodic,chaotic,hyperchaotic,and quasi-periodic oscillations,as well as initial-offset-regulated multistability.We derive sufficient conditions for achieving exponential synchronization and identify multiple synchronous regimes with transitions that strongly depend on the initial states.Field-programmable gate array(FPGA)implementation confirms the predicted dynamics and synchronization in real time,demonstrating that the memristive coupler enables complex dynamics and controllable synchronization in the most compact Hopfield architecture,with implications for the study of neuromorphic circuits and synchronization.展开更多
The functionality of the biological brain is closely related to the dynamic behavior generated by synapses in its complex neural system.The self-connection synapse,as a critical form of feedback synapse in Hopfield ne...The functionality of the biological brain is closely related to the dynamic behavior generated by synapses in its complex neural system.The self-connection synapse,as a critical form of feedback synapse in Hopfield neurons,plays an essential role in understanding the dynamic behavior of the brain.Synaptic memristors can bring neural network models closer to the complexity of the brain's neural networks.Inspired by this,this study incorporates the nonlinear memory characteristics of synapses into the Hopfield neural network(HNN)by replacing a single self-synapse in a four-dimensional HNN model with a novel cosine memristor model,aiming to more realistically reproduce the dynamical behavior of biological neurons in artificial systems.By performing a dynamical analysis of the system using numerical methods,we find that the model exhibits infinitely many equilibrium points and can induce the formation of rare transient attractors,as well as an arbitrary number of multi-scroll attractors.Additionally,the model demonstrates complex coexisting attractor dynamics,including transient chaos,periodicity,decaying periodicity,and coexisting chaos.Furthermore,the feasibility of the proposed HNN model is verified using a field-programmable gate array(FPGA).Finally,an electronic codebook(ECB)–mode block cipher encryption algorithm is proposed for image encryption.The encryption performance is evaluated,with an information entropy value of 7.9993,demonstrating the excellent randomness of the system-generated numbers.展开更多
文摘本文旨在研究分数阶Hopfield神经网络(Fractional order Hopfield neural networks,FHNN)的Hyers-Ulam-Rassias稳定性.利用Mittag-Leffler函数和Gronwall估计定理,给出了当神经元激活函数满足Lipschitz条件时,神经网络满足Hyers-Ulam-Rassias稳定性的一个充分条件,从而提供了一种通过验证自反馈系数矩阵和权重系数矩阵判断神经网络具有Hyers-Ulam稳定性的方法.最后,本文设置满足定理的神经网络系数,利用仿真实验,验证此充分条件的正确性.
文摘The large-scale acquisition and widespread application of remote sensing image data have led to increasingly severe challenges in information security and privacy protection during transmission and storage.Urban remote sensing image,characterized by complex content and well-defined structures,are particularly vulnerable to malicious attacks and information leakage.To address this issue,the author proposes an encryption method based on the enhanced single-neuron dynamical system(ESNDS).ESNDS generates highquality pseudo-random sequences with complex dynamics and intense sensitivity to initial conditions,which drive a structure of multi-stage cipher comprising permutation,ring-wise diffusion,and mask perturbation.Using representative GF-2 Panchromatic and Multispectral Scanner(PMS)urban scenes,the author conducts systematic evaluations in terms of inter-pixel correlation,information entropy,histogram uniformity,and number of pixel change rate(NPCR)/unified average changing intensity(UACI).The results demonstrate that the proposed scheme effectively resists statistical analysis,differential attacks,and known-plaintext attacks while maintaining competitive computational efficiency for high-resolution urban image.In addition,the cipher is lightweight and hardware-friendly,integrates readily with on-board and ground processing,and thus offers tangible engineering utility for real-time,large-volume remote-sensing data protection.
基金supported by the National Natural Science Foundation of China(Grant No.62271088)the Qinglan Project of Jiangsu Province+2 种基金the Jiangsu Government Scholarship for Overseas Studiesthe Training Plan of Young Backbone Teachers in Universities of Henan Province(Grant No.2023GGJS142)the Key Scientific Research of Colleges and Universities in Henan Province(Grant No.25A120009)。
文摘Neural synchronization is associated with various brain disorders,making it essential to investigate the intrinsic factors that influence the synchronization of coupled neural networks.In this paper,we propose a minimal architecture as a prototype,consisting of two bi-neuron Hopfield neural networks(HNNs)coupled via a memristor.This coupling elevates the original two bi-neuron HNNs into a five-dimensional system,featuring an unstable line equilibrium set and rich dynamics absent in the uncoupled case.Our results show that varying the coupling strength and the initial state of the memristor can induce periodic,chaotic,hyperchaotic,and quasi-periodic oscillations,as well as initial-offset-regulated multistability.We derive sufficient conditions for achieving exponential synchronization and identify multiple synchronous regimes with transitions that strongly depend on the initial states.Field-programmable gate array(FPGA)implementation confirms the predicted dynamics and synchronization in real time,demonstrating that the memristive coupler enables complex dynamics and controllable synchronization in the most compact Hopfield architecture,with implications for the study of neuromorphic circuits and synchronization.
基金supported by the Guiding Science and Technology Plan Project of Changsha City under Grant kzd2501129by the Natural Science Foundation of Hunan Province(Grant No.2025JJ50368)+1 种基金the Scientific Research Fund of Hunan Provincial Education Department(Grant No.24A0248)the National Natural Science Foundation of China(Grant No.62273141)。
文摘The functionality of the biological brain is closely related to the dynamic behavior generated by synapses in its complex neural system.The self-connection synapse,as a critical form of feedback synapse in Hopfield neurons,plays an essential role in understanding the dynamic behavior of the brain.Synaptic memristors can bring neural network models closer to the complexity of the brain's neural networks.Inspired by this,this study incorporates the nonlinear memory characteristics of synapses into the Hopfield neural network(HNN)by replacing a single self-synapse in a four-dimensional HNN model with a novel cosine memristor model,aiming to more realistically reproduce the dynamical behavior of biological neurons in artificial systems.By performing a dynamical analysis of the system using numerical methods,we find that the model exhibits infinitely many equilibrium points and can induce the formation of rare transient attractors,as well as an arbitrary number of multi-scroll attractors.Additionally,the model demonstrates complex coexisting attractor dynamics,including transient chaos,periodicity,decaying periodicity,and coexisting chaos.Furthermore,the feasibility of the proposed HNN model is verified using a field-programmable gate array(FPGA).Finally,an electronic codebook(ECB)–mode block cipher encryption algorithm is proposed for image encryption.The encryption performance is evaluated,with an information entropy value of 7.9993,demonstrating the excellent randomness of the system-generated numbers.
