In this paper, the modified projective synchronization （MPS） of a fractional-order hyperchaotic system is inves- tigated. We design the response system corresponding to the drive system on the basis of projective sy...In this paper, the modified projective synchronization （MPS） of a fractional-order hyperchaotic system is inves- tigated. We design the response system corresponding to the drive system on the basis of projective synchronization theory, and determine the sufficient condition for the synchronization of the drive system and the response system based on fractional-order stability theory. The MPS of a fractional-order hyperchaotic system is achieved by transmitting a single variable. This scheme reduces the information transmission in order to achieve the synchronization, and extends the applicable scope of MPS. Numerical simulations further demonstrate the feasibility and the effectiveness of the proposed scheme.展开更多
In this paper, a novel hyperchaotic system with one nonlinear term and its fractional order system are proposed. Furthermore,synchronization between two fractional-order systems with different fractional-order values ...In this paper, a novel hyperchaotic system with one nonlinear term and its fractional order system are proposed. Furthermore,synchronization between two fractional-order systems with different fractional-order values is achieved. The proposed synchronization scheme is simple and theoretically rigorous.Numerical simulations are in agreement with the theoretical analysis.展开更多
In this paper, an impulsive synchronisation scheme for a class of fractional-order hyperchaotic systems is proposed. The sufficient conditions of a class of integral-order hyperchaotic systems＇ impulsive synchronisat...In this paper, an impulsive synchronisation scheme for a class of fractional-order hyperchaotic systems is proposed. The sufficient conditions of a class of integral-order hyperchaotic systems＇ impulsive synchronisation are illustrated. Furthermore, we apply the sufficient conditions to a class of fractional-order hyperchaotic systems and well achieve impulsive synchronisation of these fractional-order hyperchaotic systems, thereby extending the applicable scope of impulsive synchronisation. Numerical simulations further demonstrate the feasibility and effectiveness of the proposed scheme.展开更多
In this paper, Adomian decomposition method （ADM） with high accuracy and fast convergence is introduced to solve the fractional-order piecewise-linear （PWL） hyperchaotic system. Based on the obtained hyperchaotic ...In this paper, Adomian decomposition method （ADM） with high accuracy and fast convergence is introduced to solve the fractional-order piecewise-linear （PWL） hyperchaotic system. Based on the obtained hyperchaotic sequences, a novel color image encryption algorithm is proposed by employing a hybrid model of bidirectional circular permutation and DNA masking. In this scheme, the pixel positions of image are scrambled by circular permutation, and the pixel values are substituted by DNA sequence operations. In the DNA sequence operations, addition and substraction operations are performed according to traditional addition and subtraction in the binary, and two rounds of addition rules are used to encrypt the pixel values. The simulation results and security analysis show that the hyperchaotic map is suitable for image encryption, and the proposed encryption algorithm has good encryption effect and strong key sensitivity. It can resist brute-force attack, statistical attack, differential attack, known-plaintext, and chosen-plaintext attacks.展开更多
In this paper,a simplest fractional-order hyperchaotic(SFOH)system is obtained when the fractional calculus is applied to the piecewise-linear hyperchaotic system,which possesses seven terms without any quadratic or h...In this paper,a simplest fractional-order hyperchaotic(SFOH)system is obtained when the fractional calculus is applied to the piecewise-linear hyperchaotic system,which possesses seven terms without any quadratic or higher-order polynomials.The numerical solution of the SFOH system is investigated based on the Adomian decomposition method(ADM).The methods of segmentation and replacement function are proposed to solve this system and analyze the dynamics.Dynamics of this system are demonstrated by means of phase portraits,bifurcation diagrams,Lyapunov exponent spectrum(LEs)and Poincarésection.The results show that the system has a wide chaotic range with order change,and large Lyapunov exponent when the order is very small,which indicates that the system has a good application prospect.Besides,the parameter a is a partial amplitude controller for the SFOH system.Finally,the system is successfully implemented by digital signal processor(DSP).It lays a foundation for the application of the SFOH system.展开更多
The purpose of this paper is to analyze the dynamic behavior of fractional-order four-order hyperchaotic Lii system, and use the Open-Plus-Closed-Looping （OPCL） coupling method to construct the system＇s correspondi...The purpose of this paper is to analyze the dynamic behavior of fractional-order four-order hyperchaotic Lii system, and use the Open-Plus-Closed-Looping （OPCL） coupling method to construct the system＇s corresponding response system, and then implement function projective synchronization （FPS） of fractional-order drive-response system with system parameters perturbation or not. Finally, the numerical simulations verify the effectiveness and robustness of this scheme.展开更多
We propose a new image encryption algorithm on the basis of the fractional-order hyperchaotic Lorenz system. While in the process of generating a key stream, the system parameters and the derivative order are embedded...We propose a new image encryption algorithm on the basis of the fractional-order hyperchaotic Lorenz system. While in the process of generating a key stream, the system parameters and the derivative order are embedded in the proposed algorithm to enhance the security. Such an algorithm is detailed in terms of security analyses, including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. The experimental results demonstrate that the proposed image encryption scheme has the advantages of large key space and high security for practical image encryption.展开更多
Investigating the combined effects of mining damage and creep damage on slope stability is crucial,as it can comprehensively reveal the non-linear deformation characteristics of rock under their joint influence.This s...Investigating the combined effects of mining damage and creep damage on slope stability is crucial,as it can comprehensively reveal the non-linear deformation characteristics of rock under their joint influence.This study develops a fractional-order nonlinear creep constitutive model that incorporates the double damage effect and implements a non-linear creep subroutine for soft rock using the threedimensional finite difference method on the FLAC3D platform.Comparative analysis of the theoretical,numerical,and experimental results reveals that the fractional-order constitutive model,which incorporates the double damage effect,accurately reflects the distinct deformation stages of green mudstone during creep failure and effectively captures the non-linear deformation in the accelerated creep phase.The numerical results show a fitting accuracy exceeding 97%with the creep test curves,significantly outperforming the 61%accuracy of traditional creep models.展开更多
In this paper,a fractional-order kinematic model is utilized to capture the size-dependent static bending and free vibration responses of piezoelectric nanobeams.The general nonlocal strains in the Euler-Bernoulli pie...In this paper,a fractional-order kinematic model is utilized to capture the size-dependent static bending and free vibration responses of piezoelectric nanobeams.The general nonlocal strains in the Euler-Bernoulli piezoelectric beam are defined by a frame-invariant and dimensionally consistent Riesz-Caputo fractional-order derivatives.The strain energy,the work done by external loads,and the kinetic energy based on the fractional-order kinematic model are derived and expressed in explicit forms.The boundary conditions for the nonlocal Euler-Bernoulli beam are derived through variational principles.Furthermore,a finite element model for the fractional-order system is developed in order to obtain the numerical solutions to the integro-differential equations.The effects of the fractional order and the vibration order on the static bending and vibration responses of the Euler-Bernoulli piezoelectric beams are investigated numerically.The results from the present model are validated against the existing results in the literature,and it is demonstrated that they are theoretically consistent.Although this fractional finite element method(FEM)is presented in the context of a one-dimensional(1D)beam,it can be extended to higher dimensional fractional-order boundary value problems.展开更多
Since the method of discretizing memristors was proposed,discrete memristors(DMs)have become a very important topic in recent years.However,there has been little research on non-autonomous discrete memristors(NDMs)and...Since the method of discretizing memristors was proposed,discrete memristors(DMs)have become a very important topic in recent years.However,there has been little research on non-autonomous discrete memristors(NDMs)and their applications.Therefore,in this paper,a new NDM is constructed,and a non-autonomous hyperchaotic map is proposed by connecting this non-autonomous memristor in parallel with an autonomous memristor.This map exhibits complex dynamical behaviors,including infinitely many fixed points,initial-boosted attractors,initial-boosted bifurcations,and the size of the attractors being controlled by the initial value.In addition,a simple pseudo-random number generator(PRNG)was designed using the non-autonomous hyperchaotic map,and the pseudo-random numbers(PRNs)generated by it were tested using the National Institute of Standards and Technology(NIST)SP800-22 test suite.Finally,the non-autonomous hyperchaotic map is implemented on the STM32 hardware experimental platform.展开更多
The Industry 4.0 revolution is characterized by distributed infrastructures where data must be continuously communicated between hardware nodes and cloud servers.Specific lightweight cryptosystems are needed to protec...The Industry 4.0 revolution is characterized by distributed infrastructures where data must be continuously communicated between hardware nodes and cloud servers.Specific lightweight cryptosystems are needed to protect those links,as the hardware node tends to be resource-constrained.Then Pseudo Random Number Generators are employed to produce random keys,whose final behavior depends on the initial seed.To guarantee good mathematical behavior,most key generators need an unpredictable voltage signal as input.However,physical signals evolve slowly and have a significant autocorrelation,so they do not have enough entropy to support highrandomness seeds.Then,electronic mechanisms to generate those high-entropy signals artificially are required.This paper proposes a robust hyperchaotic circuit to obtain such unpredictable electric signals.The circuit is based on a hyperchaotic dynamic system,showing a large catalog of structures,four different secret parameters,and producing four high entropy voltage signals.Synchronization schemes for the correct secret key calculation and distribution among all remote communicating modules are also analyzed and discussed.Security risks and intruder and attacker models for the proposed solution are explored,too.An experimental validation based on circuit simulations and a real hardware implementation is provided.The results show that the random properties of PRNG improved by up to 11%when seeds were calculated through the proposed circuit.展开更多
The collective dynamic of a fractional-order globally coupled system with time delays and fluctuating frequency is investigated.The power-law memory of the system is characterized using the Caputo fractional derivativ...The collective dynamic of a fractional-order globally coupled system with time delays and fluctuating frequency is investigated.The power-law memory of the system is characterized using the Caputo fractional derivative operator.Additionally,time delays in the potential field force and coupling force transmission are both considered.Firstly,based on the delay decoupling formula,combined with statistical mean method and the fractional-order Shapiro–Loginov formula,the“statistic synchronization”among particles is obtained,revealing the statistical equivalence between the mean field behavior of the system and the behavior of individual particles.Due to the existence of the coupling delay,the impact of the coupling force on synchronization exhibits non-monotonic,which is different from the previous monotonic effects.Then,two kinds of theoretical expression of output amplitude gains G and G are derived by time-delay decoupling formula and small delay approximation theorem,respectively.Compared to G,G is an exact theoretical solution,which means that G is not only more accurate in the region of small delay,but also applies to the region of large delay.Finally,the study of the output amplitude gain G and its resonance behavior are explored.Due to the presence of the potential field delay,a new resonance phenomenon termed“periodic resonance”is discovered,which arises from the periodic matching between the potential field delay and the driving frequency.This resonance phenomenon is analyzed qualitatively and quantitatively,uncovering undiscovered characteristics in previous studies.展开更多
Existing chaotic encryption schemes primarily focus on single types of images,making the design of hybrid image encryption schemes more suitable for practical applications.In this paper,a hyperchaotic map with a spher...Existing chaotic encryption schemes primarily focus on single types of images,making the design of hybrid image encryption schemes more suitable for practical applications.In this paper,a hyperchaotic map with a spherical attractor is proposed,which is constructed using spherical coordinates.Dynamical analyses reveal that the hyperchaotic map exhibits global hyperchaos and high complexity,making it capable of generating more complex chaotic sequences suitable for image encryption.A hybrid encryption scheme based on a hyperchaotic map is proposed for two-dimensional(2D)images,three-dimensional(3D)models,and 3D point clouds.Firstly,the pixels of 2D image and the coordinate data of 3D image are fused into a plaintext cube,which is combined with Hash-512 to obtain the initial value of the hyperchaotic map.Chaotic sequences are utilized for cube space internal confusion and dynamic cross-diffusion.The encrypted images demonstrate high information entropy,and the test results show that the encryption scheme effectively protects the images.The proposed hybrid image encryption scheme provides an efficient solution for securing various types of images.展开更多
Breast cancer’s heterogeneous progression demands innovative tools for accurate prediction.We present a hybrid framework that integrates machine learning(ML)and fractional-order dynamics to predict tumor growth acros...Breast cancer’s heterogeneous progression demands innovative tools for accurate prediction.We present a hybrid framework that integrates machine learning(ML)and fractional-order dynamics to predict tumor growth across diagnostic and temporal scales.On the Wisconsin Diagnostic Breast Cancer dataset,seven ML algorithms were evaluated,with deep neural networks(DNNs)achieving the highest accuracy(97.72%).Key morphological features(area,radius,texture,and concavity)were identified as top malignancy predictors,aligning with clinical intuition.Beyond static classification,we developed a fractional-order dynamical model using Caputo derivatives to capture memory-driven tumor progression.The model revealed clinically interpretable patterns:lower fractional orders correlated with prolonged aggressive growth,while higher orders indicated rapid stabilization,mimicking indolent subtypes.Theoretical analyses were rigorously proven,and numerical simulations closely fit clinical data.The framework’s clinical utility is demonstrated through an interactive graphics user interface(GUI)that integrates real-time risk assessment with growth trajectory simulations.展开更多
Deep neural network(DNN)models have achieved remarkable performance across diverse tasks,leading to widespread commercial adoption.However,training high-accuracy models demands extensive data,substantial computational...Deep neural network(DNN)models have achieved remarkable performance across diverse tasks,leading to widespread commercial adoption.However,training high-accuracy models demands extensive data,substantial computational resources,and significant time investment,making them valuable assets vulnerable to unauthorized exploitation.To address this issue,this paper proposes an intellectual property(IP)protection framework for DNN models based on feature layer selection and hyper-chaotic mapping.Firstly,a sensitivity-based importance evaluation algorithm is used to identify the key feature layers for encryption,effectively protecting the core components of the model.Next,the L1 regularization criterion is applied to further select high-weight features that significantly impact the model’s performance,ensuring that the encryption process minimizes performance loss.Finally,a dual-layer encryption mechanism is designed,introducing perturbations into the weight values and utilizing hyperchaotic mapping to disrupt channel information,further enhancing the model’s security.Experimental results demonstrate that encrypting only a small subset of parameters effectively reduces model accuracy to random-guessing levels while ensuring full recoverability.The scheme exhibits strong robustness against model pruning and fine-tuning attacks and maintains consistent performance across multiple datasets,providing an efficient and practical solution for authorization-based DNN IP protection.展开更多
To reduce the bandwidth and storage resources of image information in communication transmission, and improve the secure communication of information. In this paper, an image compression and encryption algorithm based...To reduce the bandwidth and storage resources of image information in communication transmission, and improve the secure communication of information. In this paper, an image compression and encryption algorithm based on fractional-order memristive hyperchaotic system and BP neural network is proposed. In this algorithm, the image pixel values are compressed by BP neural network, the chaotic sequences of the fractional-order memristive hyperchaotic system are used to diffuse the pixel values. The experimental simulation results indicate that the proposed algorithm not only can effectively compress and encrypt image, but also have better security features. Therefore, this work provides theoretical guidance and experimental basis for the safe transmission and storage of image information in practical communication.展开更多
This paper introduces a new four-dimensional （4D） hyperchaotic system, which has only two quadratic nonlinearity parameters but with a complex topological structure. Some complicated dynamical properties are then in...This paper introduces a new four-dimensional （4D） hyperchaotic system, which has only two quadratic nonlinearity parameters but with a complex topological structure. Some complicated dynamical properties are then investigated in detail by using bifurcations, Poincare mapping, LE spectra. Furthermore, a simple fourth-order electronic circuit is designed for hardware implementation of the 4D hyperchaotic attractors. In particular, a remarkable fractional-order circuit diagram is designed for physically verifying the hyperchaotic attractors existing not only in the integer-order system but also in the fractional-order system with an order as low as 3.6.展开更多
This paper reports a new four-dimensional hyperchaotic system obtained by adding a controller to a threedimensional autonomous chaotic system. The new system has two parameters, and each equation of the system has one...This paper reports a new four-dimensional hyperchaotic system obtained by adding a controller to a threedimensional autonomous chaotic system. The new system has two parameters, and each equation of the system has one quadratic cross-product term. Some basic properties of the new system are analysed. The different dynamic behaviours of the new system are studied when the system parameter a or b is varied. The system is hyperchaotic in several different regions of the parameter b. Especially, the two positive Lyapunov exponents are both larger, and the hyperchaotic region is also larger when this system is hyperchaotic in the case of varying a. The hyperchaotic system is analysed by Lyapunov-exponents spectrum, bifurcation diagrams and Poincaré sections.展开更多
In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive...In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.展开更多
This paper presents a novel adaptive control scheme for synchronization of the latest hyperchaotic Lü system. Based on the Lyapunov stability theory, a feedback controller and a parameter update law are designed ...This paper presents a novel adaptive control scheme for synchronization of the latest hyperchaotic Lü system. Based on the Lyapunov stability theory, a feedback controller and a parameter update law are designed for the synchronization of hyperchaotic Lfi systems with uncertainty. Numerical simulations are given to demonstrate the validity of the synchronization technique.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 60573172 and 60973152)the Superior University Doctor Subject Special Scientific Research Foundation of China (Grant No. 20070141014)the Natural Science Foundation of Liaoning Province, China (Grant No. 20082165)
文摘In this paper, the modified projective synchronization （MPS） of a fractional-order hyperchaotic system is inves- tigated. We design the response system corresponding to the drive system on the basis of projective synchronization theory, and determine the sufficient condition for the synchronization of the drive system and the response system based on fractional-order stability theory. The MPS of a fractional-order hyperchaotic system is achieved by transmitting a single variable. This scheme reduces the information transmission in order to achieve the synchronization, and extends the applicable scope of MPS. Numerical simulations further demonstrate the feasibility and the effectiveness of the proposed scheme.
基金Project supported by the Key Lab Open Foundation for Network Control Technology and Intelligent Instruments of Collegesin Chongqing Province,China (Grant No 20070F01)Education Committee of Chongqing Province,China (Grant NoKJ070502)
文摘In this paper, a novel hyperchaotic system with one nonlinear term and its fractional order system are proposed. Furthermore,synchronization between two fractional-order systems with different fractional-order values is achieved. The proposed synchronization scheme is simple and theoretically rigorous.Numerical simulations are in agreement with the theoretical analysis.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60573172 and 60973152)the Doctoral Program Foundation of the Institution of Higher Education of China (Grant No. 20070141014)the Natural Science Foundation of Liaoning Province,China (No. 20082165)
文摘In this paper, an impulsive synchronisation scheme for a class of fractional-order hyperchaotic systems is proposed. The sufficient conditions of a class of integral-order hyperchaotic systems＇ impulsive synchronisation are illustrated. Furthermore, we apply the sufficient conditions to a class of fractional-order hyperchaotic systems and well achieve impulsive synchronisation of these fractional-order hyperchaotic systems, thereby extending the applicable scope of impulsive synchronisation. Numerical simulations further demonstrate the feasibility and effectiveness of the proposed scheme.
基金supported by the National Natural Science Foundation of China(Grant Nos.61161006 and 61573383)
文摘In this paper, Adomian decomposition method （ADM） with high accuracy and fast convergence is introduced to solve the fractional-order piecewise-linear （PWL） hyperchaotic system. Based on the obtained hyperchaotic sequences, a novel color image encryption algorithm is proposed by employing a hybrid model of bidirectional circular permutation and DNA masking. In this scheme, the pixel positions of image are scrambled by circular permutation, and the pixel values are substituted by DNA sequence operations. In the DNA sequence operations, addition and substraction operations are performed according to traditional addition and subtraction in the binary, and two rounds of addition rules are used to encrypt the pixel values. The simulation results and security analysis show that the hyperchaotic map is suitable for image encryption, and the proposed encryption algorithm has good encryption effect and strong key sensitivity. It can resist brute-force attack, statistical attack, differential attack, known-plaintext, and chosen-plaintext attacks.
基金supported by the National Natural Science Foundation of China (61161006 and 61573383)supported by the Research and Innovation Project of Graduate Students of Central South University (2018ZZTS348)
文摘In this paper,a simplest fractional-order hyperchaotic(SFOH)system is obtained when the fractional calculus is applied to the piecewise-linear hyperchaotic system,which possesses seven terms without any quadratic or higher-order polynomials.The numerical solution of the SFOH system is investigated based on the Adomian decomposition method(ADM).The methods of segmentation and replacement function are proposed to solve this system and analyze the dynamics.Dynamics of this system are demonstrated by means of phase portraits,bifurcation diagrams,Lyapunov exponent spectrum(LEs)and Poincarésection.The results show that the system has a wide chaotic range with order change,and large Lyapunov exponent when the order is very small,which indicates that the system has a good application prospect.Besides,the parameter a is a partial amplitude controller for the SFOH system.Finally,the system is successfully implemented by digital signal processor(DSP).It lays a foundation for the application of the SFOH system.
基金Supported by National Natural Science Foundation of China under Grant Nos.60573172,60973152Doctoral Program Foundation of Institution of Higher Education of China under Grant No.20070141014the Natural Science Foundation of Liaoning Province of China under Grant No.20082165
文摘The purpose of this paper is to analyze the dynamic behavior of fractional-order four-order hyperchaotic Lii system, and use the Open-Plus-Closed-Looping （OPCL） coupling method to construct the system＇s corresponding response system, and then implement function projective synchronization （FPS） of fractional-order drive-response system with system parameters perturbation or not. Finally, the numerical simulations verify the effectiveness and robustness of this scheme.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61004078 and 60971022)the Natural Science Foundation of Shandong Province, China (Grant Nos. ZR2009GQ009 and ZR2009GM005)+1 种基金the China Postdoctoral Science Foundation (Grant No. 20100481293)the Special Funds for Postdoctoral Innovative Projects of Shandong Province, China (Grant No. 201003037)
文摘We propose a new image encryption algorithm on the basis of the fractional-order hyperchaotic Lorenz system. While in the process of generating a key stream, the system parameters and the derivative order are embedded in the proposed algorithm to enhance the security. Such an algorithm is detailed in terms of security analyses, including correlation analysis, information entropy analysis, run statistic analysis, mean-variance gray value analysis, and key sensitivity analysis. The experimental results demonstrate that the proposed image encryption scheme has the advantages of large key space and high security for practical image encryption.
基金support from the National Natural Science Foundation of China(No.52308316)the Scientific Research Foundation of Weifang University(Grant No.2024BS42)+2 种基金China Postdoctoral Science Foundation(No.2022M721885)the Key Laboratory of Rock Mechanics and Geohazards of Zhejiang Province(No.ZJRMG-2022-01)supported by Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences(NO.SKLGME023017).
文摘Investigating the combined effects of mining damage and creep damage on slope stability is crucial,as it can comprehensively reveal the non-linear deformation characteristics of rock under their joint influence.This study develops a fractional-order nonlinear creep constitutive model that incorporates the double damage effect and implements a non-linear creep subroutine for soft rock using the threedimensional finite difference method on the FLAC3D platform.Comparative analysis of the theoretical,numerical,and experimental results reveals that the fractional-order constitutive model,which incorporates the double damage effect,accurately reflects the distinct deformation stages of green mudstone during creep failure and effectively captures the non-linear deformation in the accelerated creep phase.The numerical results show a fitting accuracy exceeding 97%with the creep test curves,significantly outperforming the 61%accuracy of traditional creep models.
基金Project supported by the National Natural Science Foundation of China(No.12172169)。
文摘In this paper,a fractional-order kinematic model is utilized to capture the size-dependent static bending and free vibration responses of piezoelectric nanobeams.The general nonlocal strains in the Euler-Bernoulli piezoelectric beam are defined by a frame-invariant and dimensionally consistent Riesz-Caputo fractional-order derivatives.The strain energy,the work done by external loads,and the kinetic energy based on the fractional-order kinematic model are derived and expressed in explicit forms.The boundary conditions for the nonlocal Euler-Bernoulli beam are derived through variational principles.Furthermore,a finite element model for the fractional-order system is developed in order to obtain the numerical solutions to the integro-differential equations.The effects of the fractional order and the vibration order on the static bending and vibration responses of the Euler-Bernoulli piezoelectric beams are investigated numerically.The results from the present model are validated against the existing results in the literature,and it is demonstrated that they are theoretically consistent.Although this fractional finite element method(FEM)is presented in the context of a one-dimensional(1D)beam,it can be extended to higher dimensional fractional-order boundary value problems.
基金supported by the National Natural Science Foundation of China(Grant No.62071411).
文摘Since the method of discretizing memristors was proposed,discrete memristors(DMs)have become a very important topic in recent years.However,there has been little research on non-autonomous discrete memristors(NDMs)and their applications.Therefore,in this paper,a new NDM is constructed,and a non-autonomous hyperchaotic map is proposed by connecting this non-autonomous memristor in parallel with an autonomous memristor.This map exhibits complex dynamical behaviors,including infinitely many fixed points,initial-boosted attractors,initial-boosted bifurcations,and the size of the attractors being controlled by the initial value.In addition,a simple pseudo-random number generator(PRNG)was designed using the non-autonomous hyperchaotic map,and the pseudo-random numbers(PRNs)generated by it were tested using the National Institute of Standards and Technology(NIST)SP800-22 test suite.Finally,the non-autonomous hyperchaotic map is implemented on the STM32 hardware experimental platform.
基金supported by Comunidad de Madrid within the framework of the Multiannual Agreement with Universidad Politecnica de Madrid to encourage research by young doctors(PRINCE).
文摘The Industry 4.0 revolution is characterized by distributed infrastructures where data must be continuously communicated between hardware nodes and cloud servers.Specific lightweight cryptosystems are needed to protect those links,as the hardware node tends to be resource-constrained.Then Pseudo Random Number Generators are employed to produce random keys,whose final behavior depends on the initial seed.To guarantee good mathematical behavior,most key generators need an unpredictable voltage signal as input.However,physical signals evolve slowly and have a significant autocorrelation,so they do not have enough entropy to support highrandomness seeds.Then,electronic mechanisms to generate those high-entropy signals artificially are required.This paper proposes a robust hyperchaotic circuit to obtain such unpredictable electric signals.The circuit is based on a hyperchaotic dynamic system,showing a large catalog of structures,four different secret parameters,and producing four high entropy voltage signals.Synchronization schemes for the correct secret key calculation and distribution among all remote communicating modules are also analyzed and discussed.Security risks and intruder and attacker models for the proposed solution are explored,too.An experimental validation based on circuit simulations and a real hardware implementation is provided.The results show that the random properties of PRNG improved by up to 11%when seeds were calculated through the proposed circuit.
基金supported by the Natural Science Foundation of Sichuan Province,China(Youth Science Foundation)(Grant No.2022NSFSC1952).
文摘The collective dynamic of a fractional-order globally coupled system with time delays and fluctuating frequency is investigated.The power-law memory of the system is characterized using the Caputo fractional derivative operator.Additionally,time delays in the potential field force and coupling force transmission are both considered.Firstly,based on the delay decoupling formula,combined with statistical mean method and the fractional-order Shapiro–Loginov formula,the“statistic synchronization”among particles is obtained,revealing the statistical equivalence between the mean field behavior of the system and the behavior of individual particles.Due to the existence of the coupling delay,the impact of the coupling force on synchronization exhibits non-monotonic,which is different from the previous monotonic effects.Then,two kinds of theoretical expression of output amplitude gains G and G are derived by time-delay decoupling formula and small delay approximation theorem,respectively.Compared to G,G is an exact theoretical solution,which means that G is not only more accurate in the region of small delay,but also applies to the region of large delay.Finally,the study of the output amplitude gain G and its resonance behavior are explored.Due to the presence of the potential field delay,a new resonance phenomenon termed“periodic resonance”is discovered,which arises from the periodic matching between the potential field delay and the driving frequency.This resonance phenomenon is analyzed qualitatively and quantitatively,uncovering undiscovered characteristics in previous studies.
基金Project supported by the Basic Scientific Research Projects of Department of Education of Liaoning Province,China(Grant No.LJ212410152049)the Technological Innovation Projects in the field of artificial intelligence of Liaoning Province,China(Grant No.2023JH26/10300011)。
文摘Existing chaotic encryption schemes primarily focus on single types of images,making the design of hybrid image encryption schemes more suitable for practical applications.In this paper,a hyperchaotic map with a spherical attractor is proposed,which is constructed using spherical coordinates.Dynamical analyses reveal that the hyperchaotic map exhibits global hyperchaos and high complexity,making it capable of generating more complex chaotic sequences suitable for image encryption.A hybrid encryption scheme based on a hyperchaotic map is proposed for two-dimensional(2D)images,three-dimensional(3D)models,and 3D point clouds.Firstly,the pixels of 2D image and the coordinate data of 3D image are fused into a plaintext cube,which is combined with Hash-512 to obtain the initial value of the hyperchaotic map.Chaotic sequences are utilized for cube space internal confusion and dynamic cross-diffusion.The encrypted images demonstrate high information entropy,and the test results show that the encryption scheme effectively protects the images.The proposed hybrid image encryption scheme provides an efficient solution for securing various types of images.
文摘Breast cancer’s heterogeneous progression demands innovative tools for accurate prediction.We present a hybrid framework that integrates machine learning(ML)and fractional-order dynamics to predict tumor growth across diagnostic and temporal scales.On the Wisconsin Diagnostic Breast Cancer dataset,seven ML algorithms were evaluated,with deep neural networks(DNNs)achieving the highest accuracy(97.72%).Key morphological features(area,radius,texture,and concavity)were identified as top malignancy predictors,aligning with clinical intuition.Beyond static classification,we developed a fractional-order dynamical model using Caputo derivatives to capture memory-driven tumor progression.The model revealed clinically interpretable patterns:lower fractional orders correlated with prolonged aggressive growth,while higher orders indicated rapid stabilization,mimicking indolent subtypes.Theoretical analyses were rigorously proven,and numerical simulations closely fit clinical data.The framework’s clinical utility is demonstrated through an interactive graphics user interface(GUI)that integrates real-time risk assessment with growth trajectory simulations.
基金supported in part by the National Natural Science Foundation of China under Grant No.62172280in part by the Key Scientific Research Projects of Colleges and Universities in Henan Province,China under Grant No.23A520006in part by Henan Provincial Science and Technology Research Project under Grant No.222102210199.
文摘Deep neural network(DNN)models have achieved remarkable performance across diverse tasks,leading to widespread commercial adoption.However,training high-accuracy models demands extensive data,substantial computational resources,and significant time investment,making them valuable assets vulnerable to unauthorized exploitation.To address this issue,this paper proposes an intellectual property(IP)protection framework for DNN models based on feature layer selection and hyper-chaotic mapping.Firstly,a sensitivity-based importance evaluation algorithm is used to identify the key feature layers for encryption,effectively protecting the core components of the model.Next,the L1 regularization criterion is applied to further select high-weight features that significantly impact the model’s performance,ensuring that the encryption process minimizes performance loss.Finally,a dual-layer encryption mechanism is designed,introducing perturbations into the weight values and utilizing hyperchaotic mapping to disrupt channel information,further enhancing the model’s security.Experimental results demonstrate that encrypting only a small subset of parameters effectively reduces model accuracy to random-guessing levels while ensuring full recoverability.The scheme exhibits strong robustness against model pruning and fine-tuning attacks and maintains consistent performance across multiple datasets,providing an efficient and practical solution for authorization-based DNN IP protection.
基金the Basic Scientific Research Projects of Colleges and Universities of Liaoning Province (Grant Nos. 2017J045)Provincial Natural Science Foundation of Liaoning (Grant Nos. 20170540060)
文摘To reduce the bandwidth and storage resources of image information in communication transmission, and improve the secure communication of information. In this paper, an image compression and encryption algorithm based on fractional-order memristive hyperchaotic system and BP neural network is proposed. In this algorithm, the image pixel values are compressed by BP neural network, the chaotic sequences of the fractional-order memristive hyperchaotic system are used to diffuse the pixel values. The experimental simulation results indicate that the proposed algorithm not only can effectively compress and encrypt image, but also have better security features. Therefore, this work provides theoretical guidance and experimental basis for the safe transmission and storage of image information in practical communication.
文摘This paper introduces a new four-dimensional （4D） hyperchaotic system, which has only two quadratic nonlinearity parameters but with a complex topological structure. Some complicated dynamical properties are then investigated in detail by using bifurcations, Poincare mapping, LE spectra. Furthermore, a simple fourth-order electronic circuit is designed for hardware implementation of the 4D hyperchaotic attractors. In particular, a remarkable fractional-order circuit diagram is designed for physically verifying the hyperchaotic attractors existing not only in the integer-order system but also in the fractional-order system with an order as low as 3.6.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 60374037 and 60574036）, the Specialized Research Fund for the Doctoral Program of China （Grant No 20050055013） and the Program for New Century Excellent Talents in University of China （NCET）.
文摘This paper reports a new four-dimensional hyperchaotic system obtained by adding a controller to a threedimensional autonomous chaotic system. The new system has two parameters, and each equation of the system has one quadratic cross-product term. Some basic properties of the new system are analysed. The different dynamic behaviours of the new system are studied when the system parameter a or b is varied. The system is hyperchaotic in several different regions of the parameter b. Especially, the two positive Lyapunov exponents are both larger, and the hyperchaotic region is also larger when this system is hyperchaotic in the case of varying a. The hyperchaotic system is analysed by Lyapunov-exponents spectrum, bifurcation diagrams and Poincaré sections.
基金Project supported by the National Natural Science Foundation of China （Grant No 60574045） and partly by Foundation of Guangxi Department of Education, China （Grant No （2006）26-118）.
文摘In this paper is investigated the generalized projective synchronization of a class of chaotic （or hyperchaotic） systems, in which certain parameters can be separated from uncertain parameters. Based on the adaptive technique, the globally generalized projective synchronization of two identical chaotic （hyperchaotic） systems is achieved by designing a novel nonlinear controller. Furthermore, the parameter identification is realized simultaneously. A sufficient condition for the globally projective synchronization is obtained. Finally, by taking the hyperchaotic L system as example, some numerical simulations are provided to demonstrate the effectiveness and feasibility of the proposed technique.
基金Project supported by the National Natural Science Foundation of China （Grant No 60574045）.
文摘This paper presents a novel adaptive control scheme for synchronization of the latest hyperchaotic Lü system. Based on the Lyapunov stability theory, a feedback controller and a parameter update law are designed for the synchronization of hyperchaotic Lfi systems with uncertainty. Numerical simulations are given to demonstrate the validity of the synchronization technique.
