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A novel four-wing chaotic attractor generated from a three-dimensional quadratic autonomous system 被引量:12
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作者 董恩增 陈在平 +1 位作者 陈增强 袁著祉 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第7期2680-2689,共10页
This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide... This paper presents a new 3D quadratic autonomous chaotic system which contains five system parameters and three quadratic cross-product terms,and the system can generate a single four-wing chaotic attractor with wide parameter ranges. Through theoretical analysis,the Hopf bifurcation processes are proved to arise at certain equilibrium points.Numerical bifurcation analysis shows that the system has many interesting complex dynamical behaviours;the system trajectory can evolve to a chaotic attractor from a periodic orbit or a fixed point as the proper parameter varies. Finally,an analog electronic circuit is designed to physically realize the chaotic system;the existence of four-wing chaotic attractor is verified by the analog circuit realization. 展开更多
关键词 CHAOS four-wing chaotic attractor bifurcation analysis chaotic circuit
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Hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system 被引量:10
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作者 薛薇 齐国元 +2 位作者 沐晶晶 贾红艳 郭彦岭 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第8期325-332,共8页
In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter va... In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincare maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a Hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system. 展开更多
关键词 HYPER-CHAOS four-wing chaotic system one equilibrium Hopf bifurcation circuit implementation
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Novel four-wing and eight-wing attractors using coupled chaotic Lorenz systems 被引量:2
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作者 Giuseppe Grassi 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第9期3247-3251,共5页
This paper presents the problem of generating four-wing (eight-wing) chaotic attractors. The adopted method consists in suitably coupling two (three) identical Lorenz systems. In analogy with the original Lorenz s... This paper presents the problem of generating four-wing (eight-wing) chaotic attractors. The adopted method consists in suitably coupling two (three) identical Lorenz systems. In analogy with the original Lorenz system, where the two wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four wings (eight wings) of these novel attractors axe located around the four (eight) equilibria with two (three) pairs of unstable complex-conjugate eigenvalues. 展开更多
关键词 chaotic attractors multi-wing attractor coupled Lorenz systems dynamical behaviours
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Novel four-dimensional autonomous chaotic system generating one-,two-,three- and four-wing attractors 被引量:1
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作者 余飞 王春华 +1 位作者 尹晋文 徐浩 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第11期151-158,共8页
In this paper, we propose a novel four-dimensional autonomous chaotic system. Of particular interest is that this novel system can generate one-, two, three- and four-wing chaotic attractors with the variation of a si... In this paper, we propose a novel four-dimensional autonomous chaotic system. Of particular interest is that this novel system can generate one-, two, three- and four-wing chaotic attractors with the variation of a single parameter, and the multi-wing type of the chaotic attractors can be displayed in all directions. The system is simple with a large positive Lyapunov exponent and can exhibit some interesting and complicated dynamical behaviours. Basic dynamical properties of the four-dimensional chaotic system, such as equilibrium points, the Poincare map, the bifurcation diagram and the Lyapunov exponents are investigated by using either theoretical analysis or numerical method. Finally, a circuit is designed for the implementation of the multi-wing chaotic attractors. The electronic workbench observations axe in good agreement with the numerical simulation results. 展开更多
关键词 multi-wing chaotic attractors four-dimensional chaotic system Poincare map bifurcation diagram
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Topological horseshoe analysis and field-programmable gate array implementation of a fractional-order four-wing chaotic attractor 被引量:1
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作者 董恩增 王震 +2 位作者 于晓 陈增强 王增会 《Chinese Physics B》 SCIE EI CAS CSCD 2018年第1期300-306,共7页
We present a fractional-order three-dimensional chaotic system, which can generate four-wing chaotic attractor. Dy- namics of the fractional-order system is investigated by numerical simulations. To rigorously verify ... We present a fractional-order three-dimensional chaotic system, which can generate four-wing chaotic attractor. Dy- namics of the fractional-order system is investigated by numerical simulations. To rigorously verify the chaos properties of this system, the existence of horseshoe in the four-wing attractor is presented. Firstly, a Poincar6 section is selected properly, and a first-return Poincar6 map is established. Then, a one-dimensional tensile horseshoe is discovered, which verifies the chaos existence of the system in mathematical view. Finally, the fractional-order chaotic attractor is imple- mented physically with a field-programmable gate array (FPGA) chip, which is useful in further engineering applications of information encryption and secure communications. 展开更多
关键词 fractional-order chaotic system Poincar6 map topological horseshoe field-programmable gatearray (FPGA)
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Chaotic CS Encryption:An Efficient Image Encryption Algorithm Based on Chebyshev Chaotic System and Compressive Sensing
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作者 Mingliang Sun Jie Yuan +1 位作者 Xiaoyong Li Dongxiao Liu 《Computers, Materials & Continua》 SCIE EI 2024年第5期2625-2646,共22页
Images are the most important carrier of human information. Moreover, how to safely transmit digital imagesthrough public channels has become an urgent problem. In this paper, we propose a novel image encryptionalgori... Images are the most important carrier of human information. Moreover, how to safely transmit digital imagesthrough public channels has become an urgent problem. In this paper, we propose a novel image encryptionalgorithm, called chaotic compressive sensing (CS) encryption (CCSE), which can not only improve the efficiencyof image transmission but also introduce the high security of the chaotic system. Specifically, the proposed CCSEcan fully leverage the advantages of the Chebyshev chaotic system and CS, enabling it to withstand various attacks,such as differential attacks, and exhibit robustness. First, we use a sparse trans-form to sparse the plaintext imageand then use theArnold transformto perturb the image pixels. After that,we elaborate aChebyshev Toeplitz chaoticsensing matrix for CCSE. By using this Toeplitz matrix, the perturbed image is compressed and sampled to reducethe transmission bandwidth and the amount of data. Finally, a bilateral diffusion operator and a chaotic encryptionoperator are used to perturb and expand the image pixels to change the pixel position and value of the compressedimage, and ultimately obtain an encrypted image. Experimental results show that our method can be resistant tovarious attacks, such as the statistical attack and noise attack, and can outperform its current competitors. 展开更多
关键词 Image encryption chaotic system compressive sensing arnold transform
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Double quantum images encryption scheme based on chaotic system
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作者 蒋社想 李杨 +1 位作者 石锦 张茹 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第4期305-320,共16页
This paper explores a double quantum images representation(DNEQR)model that allows for simultaneous storage of two digital images in a quantum superposition state.Additionally,a new type of two-dimensional hyperchaoti... This paper explores a double quantum images representation(DNEQR)model that allows for simultaneous storage of two digital images in a quantum superposition state.Additionally,a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated,offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps.Based on the DNEQR model and the hyperchaotic system,a double quantum images encryption algorithm is proposed.Firstly,two classical plaintext images are transformed into quantum states using the DNEQR model.Then,the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences.These chaotic sequences are utilized to perform pixel value and position operations on the quantum image,resulting in changes to both pixel values and positions.Finally,the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences.The corresponding quantum circuits are also given.Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission,improves the encryption efficiency,and enhances anti-interference and anti-attack capabilities. 展开更多
关键词 double quantum images encryption chaotic system pixel scrambling XOR operation
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Sliding-mode-based preassigned-time control of a class of memristor chaotic systems
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作者 Jinrong Fan Qiang Lai +1 位作者 Qiming Wang Leimin Wang 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第11期161-166,共6页
This paper addresses the preassigned-time chaos control problem of memristor chaotic systems with time delays.Since the introduction of memristor,the presented models are nonlinear systems with chaotic dynamics.First,... This paper addresses the preassigned-time chaos control problem of memristor chaotic systems with time delays.Since the introduction of memristor,the presented models are nonlinear systems with chaotic dynamics.First,the TS fuzzy method is adopted to describe the chaotic systems.Then,a sliding-model-based control approach is proposed to achieve the preassigned-time stabilization of the presented models,where the upper bound of stabilization time can be arbitrarily specified in advance.Finally,simulation results demonstrate the validity of presented control approach and theoretic results. 展开更多
关键词 memristor chaotic system TS fuzzy method preassigned-time stabilization sliding-mode control
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Chaotic Map-Based Authentication and Key Agreement Protocol with Low-Latency for Metasystem
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作者 Guojun Wang Qi Liu 《Computers, Materials & Continua》 SCIE EI 2024年第3期4471-4488,共18页
With the rapid advancement in exploring perceptual interactions and digital twins,metaverse technology has emerged to transcend the constraints of space-time and reality,facilitating remote AI-based collaboration.In t... With the rapid advancement in exploring perceptual interactions and digital twins,metaverse technology has emerged to transcend the constraints of space-time and reality,facilitating remote AI-based collaboration.In this dynamic metasystem environment,frequent information exchanges necessitate robust security measures,with Authentication and Key Agreement(AKA)serving as the primary line of defense to ensure communication security.However,traditional AKA protocols fall short in meeting the low-latency requirements essential for synchronous interactions within the metaverse.To address this challenge and enable nearly latency-free interactions,a novel low-latency AKA protocol based on chaotic maps is proposed.This protocol not only ensures mutual authentication of entities within the metasystem but also generates secure session keys.The security of these session keys is rigorously validated through formal proofs,formal verification,and informal proofs.When confronted with the Dolev-Yao(DY)threat model,the session keys are formally demonstrated to be secure under the Real-or-Random(ROR)model.The proposed protocol is further validated through simulations conducted using VMware workstation compiled in HLPSL language and C language.The simulation results affirm the protocol’s effectiveness in resisting well-known attacks while achieving the desired low latency for optimal metaverse interactions. 展开更多
关键词 Metasystem authentication and key agreement chaotic map secure communication
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CNN-LSTM based incremental attention mechanism enabled phase-space reconstruction for chaotic time series prediction
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作者 Xiao-Qian Lu Jun Tian +2 位作者 Qiang Liao Zheng-Wu Xu Lu Gan 《Journal of Electronic Science and Technology》 EI CAS CSCD 2024年第2期77-90,共14页
To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network,we propose a convolutional neural network-long short-term memory(CNN-LSTM)pre... To improve the prediction accuracy of chaotic time series and reconstruct a more reasonable phase space structure of the prediction network,we propose a convolutional neural network-long short-term memory(CNN-LSTM)prediction model based on the incremental attention mechanism.Firstly,a traversal search is conducted through the traversal layer for finite parameters in the phase space.Then,an incremental attention layer is utilized for parameter judgment based on the dimension weight criteria(DWC).The phase space parameters that best meet DWC are selected and fed into the input layer.Finally,the constructed CNN-LSTM network extracts spatio-temporal features and provides the final prediction results.The model is verified using Logistic,Lorenz,and sunspot chaotic time series,and the performance is compared from the two dimensions of prediction accuracy and network phase space structure.Additionally,the CNN-LSTM network based on incremental attention is compared with long short-term memory(LSTM),convolutional neural network(CNN),recurrent neural network(RNN),and support vector regression(SVR)for prediction accuracy.The experiment results indicate that the proposed composite network model possesses enhanced capability in extracting temporal features and achieves higher prediction accuracy.Also,the algorithm to estimate the phase space parameter is compared with the traditional CAO,false nearest neighbor,and C-C,three typical methods for determining the chaotic phase space parameters.The experiments reveal that the phase space parameter estimation algorithm based on the incremental attention mechanism is superior in prediction accuracy compared with the traditional phase space reconstruction method in five networks,including CNN-LSTM,LSTM,CNN,RNN,and SVR. 展开更多
关键词 chaotic time series Incremental attention mechanism Phase-space reconstruction
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Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode
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作者 Meiqi WU Pengyu LV +3 位作者 Hongyuan LI Jiale YAN Huiling DUAN Wei ZHANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2024年第4期581-602,共22页
The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relations... The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified.The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method.The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed.The discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coefficient,and detuning parameters,on the resonance responses.The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system.Furthermore,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare maps.Finally,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results. 展开更多
关键词 bistable laminated composite shell dynamic snap-through mode Hopf bifurcation chaotic dynamics vibration experiment
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A color image encryption scheme based on a 2D coupled chaotic system and diagonal scrambling algorithm
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作者 苏静明 方士辉 +1 位作者 洪炎 温言 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第7期233-243,共11页
A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are con... A novel color image encryption scheme is developed to enhance the security of encryption without increasing the complexity. Firstly, the plain color image is decomposed into three grayscale plain images, which are converted into the frequency domain coefficient matrices(FDCM) with discrete cosine transform(DCT) operation. After that, a twodimensional(2D) coupled chaotic system is developed and used to generate one group of embedded matrices and another group of encryption matrices, respectively. The embedded matrices are integrated with the FDCM to fulfill the frequency domain encryption, and then the inverse DCT processing is implemented to recover the spatial domain signal. Eventually,under the function of the encryption matrices and the proposed diagonal scrambling algorithm, the final color ciphertext is obtained. The experimental results show that the proposed method can not only ensure efficient encryption but also satisfy various sizes of image encryption. Besides, it has better performance than other similar techniques in statistical feature analysis, such as key space, key sensitivity, anti-differential attack, information entropy, noise attack, etc. 展开更多
关键词 color image encryption discrete cosine transform two-dimensional(2D)coupled chaotic system diagonal scrambling
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A chaotic hierarchical encryption/watermark embedding scheme for multi-medical images based on row-column confusion and closed-loop bi-directional diffusion
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作者 张哲祎 牟俊 +1 位作者 Santo Banerjee 曹颖鸿 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第2期228-237,共10页
Security during remote transmission has been an important concern for researchers in recent years.In this paper,a hierarchical encryption multi-image encryption scheme for people with different security levels is desi... Security during remote transmission has been an important concern for researchers in recent years.In this paper,a hierarchical encryption multi-image encryption scheme for people with different security levels is designed,and a multiimage encryption(MIE)algorithm with row and column confusion and closed-loop bi-directional diffusion is adopted in the paper.While ensuring secure communication of medical image information,people with different security levels have different levels of decryption keys,and differentiated visual effects can be obtained by using the strong sensitivity of chaotic keys.The highest security level can obtain decrypted images without watermarks,and at the same time,patient information and copyright attribution can be verified by obtaining watermark images.The experimental results show that the scheme is sufficiently secure as an MIE scheme with visualized differences and the encryption and decryption efficiency is significantly improved compared to other works. 展开更多
关键词 chaotic hierarchical encryption multi-medical image encryption differentiated visual effects row-column confusion closed-loop bi-directional diffusion transform domain watermark embedding
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Intrusion Detection Model Using Chaotic MAP for Network Coding Enabled Mobile Small Cells
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作者 Chanumolu Kiran Kumar Nandhakumar Ramachandran 《Computers, Materials & Continua》 SCIE EI 2024年第3期3151-3176,共26页
Wireless Network security management is difficult because of the ever-increasing number of wireless network malfunctions,vulnerabilities,and assaults.Complex security systems,such as Intrusion Detection Systems(IDS),a... Wireless Network security management is difficult because of the ever-increasing number of wireless network malfunctions,vulnerabilities,and assaults.Complex security systems,such as Intrusion Detection Systems(IDS),are essential due to the limitations of simpler security measures,such as cryptography and firewalls.Due to their compact nature and low energy reserves,wireless networks present a significant challenge for security procedures.The features of small cells can cause threats to the network.Network Coding(NC)enabled small cells are vulnerable to various types of attacks.Avoiding attacks and performing secure“peer”to“peer”data transmission is a challenging task in small cells.Due to the low power and memory requirements of the proposed model,it is well suited to use with constrained small cells.An attacker cannot change the contents of data and generate a new Hashed Homomorphic Message Authentication Code(HHMAC)hash between transmissions since the HMAC function is generated using the shared secret.In this research,a chaotic sequence mapping based low overhead 1D Improved Logistic Map is used to secure“peer”to“peer”data transmission model using lightweight H-MAC(1D-LM-P2P-LHHMAC)is proposed with accurate intrusion detection.The proposed model is evaluated with the traditional models by considering various evaluation metrics like Vector Set Generation Accuracy Levels,Key Pair Generation Time Levels,Chaotic Map Accuracy Levels,Intrusion Detection Accuracy Levels,and the results represent that the proposed model performance in chaotic map accuracy level is 98%and intrusion detection is 98.2%.The proposed model is compared with the traditional models and the results represent that the proposed model secure data transmission levels are high. 展开更多
关键词 Network coding small cells data transmission intrusion detection model hashed message authentication code chaotic sequence mapping secure transmission
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Distributional Chaoticity of the Minimal Subshift of Shift Operators
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作者 Yuanlin Chen Tianxiu Lu Jiazheng Zhao 《Journal of Applied Mathematics and Physics》 2024年第5期1647-1660,共14页
This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, d... This paper focus on the chaotic properties of minimal subshift of shift operators. It is proved that the minimal subshift of shift operators is uniformly distributional chaotic, distributional chaotic in a sequence, distributional chaotic of type k ( k∈{ 1,2,2 1 2 ,3 } ), and ( 0,1 ) -distribution. 展开更多
关键词 Shift Operators SUBSHIFT Distributional chaoticity
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Chaotic Monkey算法在局放源超声阵列定位中的应用 被引量:2
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作者 徐玉琴 张宏玮 +3 位作者 李通 杨雨龙 陶珺函 谢庆 《绝缘材料》 CAS 北大核心 2014年第5期92-95,101,共5页
由于传统的局部放电超声阵列定位方法依靠两条测向线的"测向交叉"原理进行局放源的定位,未考虑实际应用时的测向误差影响,会降低定位精度,而利用多平台测向与传统遗传算法相结合的方法进行局放源位置的搜索时,会由于遗传算法... 由于传统的局部放电超声阵列定位方法依靠两条测向线的"测向交叉"原理进行局放源的定位,未考虑实际应用时的测向误差影响,会降低定位精度,而利用多平台测向与传统遗传算法相结合的方法进行局放源位置的搜索时,会由于遗传算法易陷入局部最优而导致实用性不强。因此提出一种基于Chaotic Monkey算法的局部放电超声阵列定位方法,简要介绍了其定位原理,通过仿真分析了该方法的定位结果,并与传统遗传算法的搜索结果进行比较,验证了该方法的有效性。 展开更多
关键词 局部放电 超声阵列定位 多平台测向 chaotic Monkey算法
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A prediction comparison between univariate and multivariate chaotic time series 被引量:3
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作者 王海燕 朱梅 《Journal of Southeast University(English Edition)》 EI CAS 2003年第4期414-417,共4页
The methods to determine time delays and embedding dimensions in the phase space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic tim... The methods to determine time delays and embedding dimensions in the phase space delay reconstruction of multivariate chaotic time series are proposed. Three nonlinear prediction methods of multivariate chaotic time series including local mean prediction, local linear prediction and BP neural networks prediction are considered. The simulation results obtained by the Lorenz system show that no matter what nonlinear prediction method is used, the prediction error of multivariate chaotic time series is much smaller than the prediction error of univariate time series, even if half of the data of univariate time series are used in multivariate time series. The results also verify that methods to determine the time delays and the embedding dimensions are correct from the view of minimizing the prediction error. 展开更多
关键词 multivariate chaotic time series phase space reconstruction PREDICTION neural networks
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CHAOTIC ANNEALING NEURAL NETWORK FOR GLOBAL OPTIMIZATION OF CONSTRAINED NONLINEAR PROGRAMMING 被引量:1
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作者 张国平 王正欧 袁国林 《Transactions of Tianjin University》 EI CAS 2001年第3期141-146,共6页
Chaotic neural networks have global searching ability.But their applications are generally confined to combinatorial optimization to date.By introducing chaotic noise annealing process into conventional Hopfield netwo... Chaotic neural networks have global searching ability.But their applications are generally confined to combinatorial optimization to date.By introducing chaotic noise annealing process into conventional Hopfield network,this paper proposes a new chaotic annealing neural network (CANN) for global optimization of continuous constrained non linear programming.It is easy to implement,conceptually simple,and generally applicable.Numerical experiments on severe test functions manifest that CANN is efficient and reliable to search for global optimum and outperforms the existing genetic algorithm GAMAS for the same purpose. 展开更多
关键词 global optimization neural network chaotic noise annealing
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COMPOUND STRUCTURE OF NEW FOUR-SCROLLS CHAOTIC SYSTEM 被引量:1
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作者 刘文波 陈关荣 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2003年第2期192-195,共4页
The finding of the compound structure of a new four-scrolls chaotic system is reported, which is obtained by merging together two symmetrical attractors. And the two symmetrical attractors are generated only by adding... The finding of the compound structure of a new four-scrolls chaotic system is reported, which is obtained by merging together two symmetrical attractors. And the two symmetrical attractors are generated only by adding a constant gain to the original system. Also, the forming procedure of the new four-scrolls chaotic attractor is explored and the relation between the constant gain and the properties of the system is given. 展开更多
关键词 three-dimensional autonomous system chaotic attractor compound structure
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CHAOTIC BEHAVIOR ON REDUCTION OF PERTURBED KdV EQUATION IN FORM OF PARAMETRIC EXCITATION
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作者 周良强 陈芳启 陈予恕 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2007年第4期283-287,共5页
The chaotic dynamic behaviors of a reduction of perturbed Korteweg-de Vries (KdV) equation in form of a parametric excitation are studied. Chaotic behaviors from homoclinic crossings are analyzed with an improved Me... The chaotic dynamic behaviors of a reduction of perturbed Korteweg-de Vries (KdV) equation in form of a parametric excitation are studied. Chaotic behaviors from homoclinic crossings are analyzed with an improved Melnikov method and are compared for the systems with a periodically external excitation, with a linear periodically parametric excitation, or with a nonlinear periodically excitation. The critical curves separating chaotic regions and non-chaotic regions of the above systems are different from each other. Especially, a dead frequency is presented for the system with a nonlinear periodically parametric excitation. The chaos excited at the frequency does not occur no matter how large the excitation amplitude is. A time integration scheme is used to find the numerical solutions of these systems. Numerical results agree with the analytical ones. 展开更多
关键词 Korteweg-de Vries equation chaotic behavior Melnikov method
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