Wheeler pointed ouuailat the period of Matthews＇ chaotic function （MCF） is often too short to be suitable for crypto- graphic usage in the manner of computer statistics, but this statement was given only through di...Wheeler pointed ouuailat the period of Matthews＇ chaotic function （MCF） is often too short to be suitable for crypto- graphic usage in the manner of computer statistics, but this statement was given only through digital computation. In this paper, we proved by theoretical and practical method that period exists in MCF and analyzed the underlying reason. With two chaotic functions working together we presented a modified MCF （MMCF） that is non-periodic. The simulation tests with reconstruction of phase space showed that our modified MCF is of no period. And we described how to implement a cryptographic usage with MMCF.展开更多
This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium poin...This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point; a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle＇s invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.展开更多
A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class o...A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class of chaotic system. Self-adaptive parameter law and control law are given in the form of a theorem. The synchronization between the three-dimensional R6ssler chaotic system and the four-dimensional Chen＇s hyper-chaotic system is studied as an example for illustration. The computer simulation results demonstrate the feasibility of the method proposed.展开更多
This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projectiv...This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.展开更多
A new one-way hash function based on the unified chaotic system is constructed. With different values of a key parameter, the unified chaotic system represents different chaotic systems, based on which the one-way has...A new one-way hash function based on the unified chaotic system is constructed. With different values of a key parameter, the unified chaotic system represents different chaotic systems, based on which the one-way hash function algorithm is constructed with three round operations and an initial vector on an input message. In each round operation, the parameters are processed by three different chaotic systems generated from the unified chaotic system. Feed-forwards are used at the end of each round operation and at the end of each element of the message processing. Meanwhile, in each round operation, parameter-exchanging operations are implemented. Then, the hash value of length 160 bits is obtained from the last six parameters. Simulation and analysis both demonstrate that the algorithm has great flexibility, satisfactory hash performance, weak collision property, and high security.展开更多
In this paper, the hybrid function projective synchronization (HFPS) of different chaotic systems with uncertain periodically time-varying parameters is carried out by Fourier series expansion and adaptive bounding te...In this paper, the hybrid function projective synchronization (HFPS) of different chaotic systems with uncertain periodically time-varying parameters is carried out by Fourier series expansion and adaptive bounding technique. Fourier series expansion is used to deal with uncertain periodically time-varying parameters. Adaptive bounding technique is used to compensate the bound of truncation errors. Using the Lyapunov stability theory, an adaptive control law and six parameter updating laws are constructed to make the states of two different chaotic systems asymptotically synchronized. The control strategy does not need to know the parameters thoroughly if the time-varying parameters are periodical functions. Finally, in order to verify the effectiveness of the proposed scheme, the HFPS between Lorenz system and Chen system is completed successfully by using this scheme.展开更多
In chaotic communication system, the useful signal is hidden in chaotic signal, so the general method does not work well. Due to the random feature of chaotic signal, a functional networkbased method is presented. In ...In chaotic communication system, the useful signal is hidden in chaotic signal, so the general method does not work well. Due to the random feature of chaotic signal, a functional networkbased method is presented. In this method, the neural functions are selected from some complete function set for the functional network to reconstruct the chaotic signal, so the useful signal hidden in chaotic background is extracted. In addition, its learning algorithm is presented here and the example proves its good preformance.展开更多
A new method is presented to study the function projective lag synchronization(FPLS) of chaotic systems via adaptive-impulsive control. To achieve synchronization, suitable nonlinear adaptive-impulsive controllers are...A new method is presented to study the function projective lag synchronization(FPLS) of chaotic systems via adaptive-impulsive control. To achieve synchronization, suitable nonlinear adaptive-impulsive controllers are designed. Based on the Lyapunov stability theory and the impulsive control technology, some effective sufficient conditions are derived to ensure the drive system and the response system can be rapidly lag synchronized up to the given scaling function matrix. Numerical simulations are presented to verify the effectiveness and the feasibility of the analytical results.展开更多
针对复杂环境下无人机路径优化算法收敛精度低、全局搜索能力弱及易陷入局部最优解的问题,提出了一种改进混合蜣螂优化算法(SPM and osprey based hybrid dung beetle optimizer,SO-DBO)。使用混沌映射SPM初始化种群位置,提高算法搜索...针对复杂环境下无人机路径优化算法收敛精度低、全局搜索能力弱及易陷入局部最优解的问题,提出了一种改进混合蜣螂优化算法(SPM and osprey based hybrid dung beetle optimizer,SO-DBO)。使用混沌映射SPM初始化种群位置,提高算法搜索效率。在滚球蜣螂种群有障碍模式和无障碍模式中分别引入动态全局勘探策略和随机角度策略,提升算法精度和全局搜索能力。在觅食蜣螂位置更新引入自适应T分布策略,增强算法逃离局部最优能力。通过动态权重因子提高算法全局搜索能力并降低陷入局部最优解的风险。实验结果表明:相比原始蜣螂优化算法(dung beetle optimizer,DBO)和粒子群算法(particle swarm optimization,PSO),改进后的SO-DBO算法代价函数指标在简单环境下分别改善了9.68%、12.93%,在复杂环境下分别改善了13.34%、17.00%,有效提升了算法的收敛速度、精度和稳定性。展开更多
The paper describes a symmetric encryption algorithm based on bit permutations and using an iterative process combined with a chaotic function. The main advantages of such a cryptosystem is its ability to encrypt secu...The paper describes a symmetric encryption algorithm based on bit permutations and using an iterative process combined with a chaotic function. The main advantages of such a cryptosystem is its ability to encrypt securely bit sequences and assuring confusion, diffusion and indistinguishability properties in the cipher. The algorithm is applied on the image encryption where the plain-image is viewed as binary sequence. The results of statistical analysis about randomness, sensitivity and correlation on the cipher-images show the relevance of the proposed cryptosystem.展开更多
The science of strategy(game theory)is known as the optimal decision-making of autonomous and challenging players in a strategic background.There are different strategies to complete the optimal decision.One of these ...The science of strategy(game theory)is known as the optimal decision-making of autonomous and challenging players in a strategic background.There are different strategies to complete the optimal decision.One of these strategies is the similarity technique.Similarity technique is a generalization of the symmetric strategy,which depends only on the other approaches employed,which can be formulated by altering diversities.One of these methods is the fractal theory.In this investigation,we present a new method studying the similarity analytic solution(SAS)of a 3D-fractal nanofluid system(FNFS).The dynamic evolution is completely given by the concept of differential subordination and majorization.Subordination andmajorization relationships are the sets of observable individualities.Game theory can simplify the conditions under which particular sets combine.We offer an explicit construction for the complex possible velocity,energy and thermal functions of two-dimensional fluid flow(the complex variable is suggested in the open unit disk,where the disk is selected at a constant temperature and concentration with uniform velocity).We establish that whenever the 3D-fractal nanofluid systemis approximated by a fractal function,the solution has the same property,so a class of fractal tangent function gives SAS.Finally,we demonstrate some simulations and examples that give the consequences of this methodology.展开更多
In this study,a new algorithm of fractional beta chaotic maps is proposed to generate chaotic sequences for image encryption.The proposed technique generates multi random sequences by shuffling the image pixel positio...In this study,a new algorithm of fractional beta chaotic maps is proposed to generate chaotic sequences for image encryption.The proposed technique generates multi random sequences by shuffling the image pixel position.This technique is used to blur the pixels connecting the input and encrypted images and to increase the attack resistance.The proposed algorithm makes the encryption process sophisticated by using fractional chaotic maps,which hold the properties of pseudo-randomness.The fractional beta sequences are utilized to alter the image pixels to decryption attacks.The experimental results proved that the proposed image encryption algorithm successfully encrypted and decrypted the images with the same keys.The output findings indicate that our proposed algorithm has good entropy and low correlation coefficients.This translates to enhanced security against different attacks.A MATLAB programming tool was used to implement and assess the image quality measures.A comparison with other image encryption techniques regarding the visual inspection and signal-to-noise ratio is provided.展开更多
基金the National Natural Science Foundation of China (60673071)
文摘Wheeler pointed ouuailat the period of Matthews＇ chaotic function （MCF） is often too short to be suitable for crypto- graphic usage in the manner of computer statistics, but this statement was given only through digital computation. In this paper, we proved by theoretical and practical method that period exists in MCF and analyzed the underlying reason. With two chaotic functions working together we presented a modified MCF （MMCF） that is non-periodic. The simulation tests with reconstruction of phase space showed that our modified MCF is of no period. And we described how to implement a cryptographic usage with MMCF.
基金Project supported by the National Natural Science Foundation of China (Grant No.61075060)the Science and Technology Research Key Program for the Education Department of Hubei Province of China (Grant No.D20105001)the Open Project of State Key Laboratory of Industrial Control Technology,China (Grant No.ICT1007)
文摘This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point; a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle＇s invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.
基金Project supported by the National Natural Science Foundation of China (Grant No 50677021)partially by the Key Project Foundation of North China Electric Power University (Grant No 20041306)by the Scientific Research Foundation for the Returned Overseas Chinese Scholar, NCEPU (Grant No 200814002)
文摘A universal adaptive generalized functional synchronization approach to any two different or identical chaotic systems with unknown parameters is proposed, based on a unified mathematical expression of a large class of chaotic system. Self-adaptive parameter law and control law are given in the form of a theorem. The synchronization between the three-dimensional R6ssler chaotic system and the four-dimensional Chen＇s hyper-chaotic system is studied as an example for illustration. The computer simulation results demonstrate the feasibility of the method proposed.
文摘This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.
基金Project supported by the Natural Science Foundation of Hunan Province,China (Grant No 08JJ4020)
文摘A new one-way hash function based on the unified chaotic system is constructed. With different values of a key parameter, the unified chaotic system represents different chaotic systems, based on which the one-way hash function algorithm is constructed with three round operations and an initial vector on an input message. In each round operation, the parameters are processed by three different chaotic systems generated from the unified chaotic system. Feed-forwards are used at the end of each round operation and at the end of each element of the message processing. Meanwhile, in each round operation, parameter-exchanging operations are implemented. Then, the hash value of length 160 bits is obtained from the last six parameters. Simulation and analysis both demonstrate that the algorithm has great flexibility, satisfactory hash performance, weak collision property, and high security.
基金supported by National Natural Science Foundation of China (No.60974139)Fundamental Research Funds for the Central Universities (No.72103676)
文摘In this paper, the hybrid function projective synchronization (HFPS) of different chaotic systems with uncertain periodically time-varying parameters is carried out by Fourier series expansion and adaptive bounding technique. Fourier series expansion is used to deal with uncertain periodically time-varying parameters. Adaptive bounding technique is used to compensate the bound of truncation errors. Using the Lyapunov stability theory, an adaptive control law and six parameter updating laws are constructed to make the states of two different chaotic systems asymptotically synchronized. The control strategy does not need to know the parameters thoroughly if the time-varying parameters are periodical functions. Finally, in order to verify the effectiveness of the proposed scheme, the HFPS between Lorenz system and Chen system is completed successfully by using this scheme.
文摘In chaotic communication system, the useful signal is hidden in chaotic signal, so the general method does not work well. Due to the random feature of chaotic signal, a functional networkbased method is presented. In this method, the neural functions are selected from some complete function set for the functional network to reconstruct the chaotic signal, so the useful signal hidden in chaotic background is extracted. In addition, its learning algorithm is presented here and the example proves its good preformance.
基金supported by National Natural Science Foundation of China (Nos. 41571417 and U1604145)Science and Technology Foundation of Henan Province of China (No. 152102210048)+3 种基金Foundation and Frontier Project of Henan Province of China (No. 162300410196)China Postdoctoral Science Foundation (No. 2016M602235)Natural Science Foundation of Educational Committee of Henan Province of China (No. 14A413015)Research Foundation of Henan University (No. xxjc20140006)
文摘A new method is presented to study the function projective lag synchronization(FPLS) of chaotic systems via adaptive-impulsive control. To achieve synchronization, suitable nonlinear adaptive-impulsive controllers are designed. Based on the Lyapunov stability theory and the impulsive control technology, some effective sufficient conditions are derived to ensure the drive system and the response system can be rapidly lag synchronized up to the given scaling function matrix. Numerical simulations are presented to verify the effectiveness and the feasibility of the analytical results.
文摘The paper describes a symmetric encryption algorithm based on bit permutations and using an iterative process combined with a chaotic function. The main advantages of such a cryptosystem is its ability to encrypt securely bit sequences and assuring confusion, diffusion and indistinguishability properties in the cipher. The algorithm is applied on the image encryption where the plain-image is viewed as binary sequence. The results of statistical analysis about randomness, sensitivity and correlation on the cipher-images show the relevance of the proposed cryptosystem.
文摘The science of strategy(game theory)is known as the optimal decision-making of autonomous and challenging players in a strategic background.There are different strategies to complete the optimal decision.One of these strategies is the similarity technique.Similarity technique is a generalization of the symmetric strategy,which depends only on the other approaches employed,which can be formulated by altering diversities.One of these methods is the fractal theory.In this investigation,we present a new method studying the similarity analytic solution(SAS)of a 3D-fractal nanofluid system(FNFS).The dynamic evolution is completely given by the concept of differential subordination and majorization.Subordination andmajorization relationships are the sets of observable individualities.Game theory can simplify the conditions under which particular sets combine.We offer an explicit construction for the complex possible velocity,energy and thermal functions of two-dimensional fluid flow(the complex variable is suggested in the open unit disk,where the disk is selected at a constant temperature and concentration with uniform velocity).We establish that whenever the 3D-fractal nanofluid systemis approximated by a fractal function,the solution has the same property,so a class of fractal tangent function gives SAS.Finally,we demonstrate some simulations and examples that give the consequences of this methodology.
文摘In this study,a new algorithm of fractional beta chaotic maps is proposed to generate chaotic sequences for image encryption.The proposed technique generates multi random sequences by shuffling the image pixel position.This technique is used to blur the pixels connecting the input and encrypted images and to increase the attack resistance.The proposed algorithm makes the encryption process sophisticated by using fractional chaotic maps,which hold the properties of pseudo-randomness.The fractional beta sequences are utilized to alter the image pixels to decryption attacks.The experimental results proved that the proposed image encryption algorithm successfully encrypted and decrypted the images with the same keys.The output findings indicate that our proposed algorithm has good entropy and low correlation coefficients.This translates to enhanced security against different attacks.A MATLAB programming tool was used to implement and assess the image quality measures.A comparison with other image encryption techniques regarding the visual inspection and signal-to-noise ratio is provided.
