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基于改进混沌麻雀搜索算法S盒与神经元电路的图像加密技术
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作者 杨超 魏霞 王聪 《计算机应用与软件》 北大核心 2024年第10期335-341,385,共8页
鉴于目前的图像加密算法所采用的S盒结构过于简单,易被破解。选用由改进的脉冲耦合尖峰神经元电路得到的混沌映射(MPSNC),并使用该映射对混沌麻雀搜索算法(CSSA)进行优化。随后,结合MPSNC映射和改进后的CSSA,设计新型的混沌S盒。最后,基... 鉴于目前的图像加密算法所采用的S盒结构过于简单,易被破解。选用由改进的脉冲耦合尖峰神经元电路得到的混沌映射(MPSNC),并使用该映射对混沌麻雀搜索算法(CSSA)进行优化。随后,结合MPSNC映射和改进后的CSSA,设计新型的混沌S盒。最后,基于MPSNC映射和新型混沌S盒构造一种图像加密算法,为增加S盒的变化,对其进行S8变换。通过迭代混沌映射生成混沌序列,使用混沌序列和S8S盒对图像进行扩散和置乱操作,得到加密后的图像。经实验验证,该加密算法参数丰富,复杂度高,并由于S盒的应用,提高了算法的非线性度,具有良好的性能,适用于图像加密。 展开更多
关键词 s 神经元电路 混沌麻雀搜索算法 混沌映射 s8变换
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Camellia密码算法S盒的量子电路优化
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作者 吕轶 罗庆斌 +1 位作者 李强 郑圆梦 《计算机科学》 CSCD 北大核心 2024年第S01期1017-1022,共6页
S盒是Camellia密码算法重要的非线性组件。使用Toffoli门、CNOT门和NOT门构建Camellia密码算法S盒的量子电路。为了降低计算的复杂度,根据S盒的代数表达式,将有限域GF(2^(8))中的乘法求逆运算同构到GF((2^(4))^(2))的复合域中的运算,构... S盒是Camellia密码算法重要的非线性组件。使用Toffoli门、CNOT门和NOT门构建Camellia密码算法S盒的量子电路。为了降低计算的复杂度,根据S盒的代数表达式,将有限域GF(2^(8))中的乘法求逆运算同构到GF((2^(4))^(2))的复合域中的运算,构造出Camellia密码算法S盒的量子电路。在优化方面,将仿射矩阵、同构矩阵以及一组CNOT门对应的矩阵先进行乘法操作,再进行综合,使用DORCIS工具优化GF(2^(4))中乘法求逆的量子电路,运用W-Type算法优化矩阵运算的量子电路。最终得到的S盒的量子电路只需使用20个量子比特,52个Toffoli门、178个CNOT门和13个NOT门,Toffoli深度为40,电路深度为130。该量子电路的正确性通过IBM公司的Aer模拟器进行验证。相比于已有的结果,文中使用的量子资源有了进一步的减少。 展开更多
关键词 量子电路 CAMELLIA s 复合域
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SM4密码算法S盒的量子电路优化 被引量:1
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作者 李强 罗庆斌 +2 位作者 吕轶 郑圆梦 沈济南 《密码学报(中英文)》 CSCD 北大核心 2024年第2期455-465,共11页
S盒是SM4密码算法中的重要非线性组件.首先基于复合域理论,将S盒代数表达式中有限域GF(2^(8))中的运算同构到复合域GF((2^(4))2)中的运算,然后使用NCT门库逐步构建并优化各个运算的量子电路,最后综合出完整的S盒量子电路.为降低Toffoli... S盒是SM4密码算法中的重要非线性组件.首先基于复合域理论,将S盒代数表达式中有限域GF(2^(8))中的运算同构到复合域GF((2^(4))2)中的运算,然后使用NCT门库逐步构建并优化各个运算的量子电路,最后综合出完整的S盒量子电路.为降低Toffoli门的使用量,根据GF(24)中乘法计算的代数表达式,选取使用Toffoli门最少的量子电路.为了降低CNOT门的使用量,主要从三方面优化:一是使用最优的CNOT电路综合出4阶矩阵的量子电路;二是采用置换矩阵法以及优化子电路的方式综合出8阶矩阵的量子电路;三是通过先合并计算再综合的思路优化整个S盒中CNOT门的数量.该S盒量子电路使用Qiskit Aer量子模拟器实现,并验证了其正确性.经量子资源分析,该优化的S盒量子电路一共使用了21个量子比特、10个NOT门、152个CNOT门和34个Toffoli门,电路深度为97.Toffoli门数量、总量子逻辑门数量、电路深度等相比已有结果都有较大减少. 展开更多
关键词 量子电路 sM4 s 复合域 优化
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AES-128中S盒变换的量子线路优化
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作者 刘建美 王洪 +3 位作者 马智 段乾恒 费洋扬 孟祥栋 《电子科技大学学报》 EI CAS CSCD 北大核心 2024年第1期144-148,共5页
使用空间资源优化的量子Karatsuba乘法来优化实现AES-128中的8×8 S盒变换,同时引入了衡量时间资源代价和空间资源代价折衷的指标——量子比特数目与T门深度之积。对实现8×8 S盒变换的分析表明,利用空间资源优化的量子Karatsub... 使用空间资源优化的量子Karatsuba乘法来优化实现AES-128中的8×8 S盒变换,同时引入了衡量时间资源代价和空间资源代价折衷的指标——量子比特数目与T门深度之积。对实现8×8 S盒变换的分析表明,利用空间资源优化的量子Karatsuba乘法的求乘法逆线路具有更优性能,其Toffoli门数目、量子比特数目、量子比特数目与T门深度之积更优。此外,使用加窗量子查表方法,进一步优化了求乘法逆以及实现S盒所需的量子资源。在此基础上,基于Qiskit分析验证了所需的量子资源。 展开更多
关键词 乘法逆 优化实现 量子线路 s
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一种非常紧凑的掩码AES的硬件设计与实现
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作者 隋谦 周佳运 +4 位作者 祝一豪 苏杨 许森 王伟嘉 《密码学报(中英文)》 CSCD 北大核心 2024年第3期662-680,共19页
差分能量分析作为一种强大的侧信道攻击手段,已经严重威胁到密码算法硬件实现的安全性,目前防护此类攻击最有效的方法就是对密码算法进行掩码处理.在AES算法中只有S盒是非线性的,因此如何安全高效地实现S盒一直是密码学领域的研究热点之... 差分能量分析作为一种强大的侧信道攻击手段,已经严重威胁到密码算法硬件实现的安全性,目前防护此类攻击最有效的方法就是对密码算法进行掩码处理.在AES算法中只有S盒是非线性的,因此如何安全高效地实现S盒一直是密码学领域的研究热点之一.本文在De Meyer等人研究工作的基础上,提出了一种具有已知最小面积的掩码S盒的串行化实现方案.先将用于零值处理的Kronecker Delta函数串行化,接着通过共享一个8位乘法器模块用于求逆以及布尔掩码和乘法掩码之间的转换,最后加上仿射变换以最小的面积代价实现了S盒.本文将S盒应用于AES算法,并且提供了掩码AES的串行化实现方案,同时给出了该方案的面积下限,在此基础上,对S盒及AES算法的部分结构进行调整,为未来的工作提供了一系列权衡面积和延迟的手段.实验表明,在可比的随机数成本下,本文S盒的一阶掩码和二阶掩码实现以一定延迟为代价将面积分别降低了48%和70%, AES算法的一阶掩码和二阶掩码实现分别降低10%和21%,并且随着安全阶数的增大,本文实现方案对面积的优化幅度会进一步提高.最后,在实验中通过对从SAKURA-G板上获取的轨迹执行固定与随机的Welch T测试来验证实现的安全性,对于AES算法的一阶掩码和二阶掩码实现分别采集了多达50万条曲线,没有发现泄漏点. 展开更多
关键词 s 掩码 AEs 侧信道攻击 电路面积
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A High Efficiency Hardware Implementation of S-Boxes Based on Composite Field for Advanced Encryption Standard
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作者 Yawen Wang Sini Bin +1 位作者 Shikai Zhu Xiaoting Hu 《Journal of Computer and Communications》 2024年第4期228-246,共19页
The SubBytes (S-box) transformation is the most crucial operation in the AES algorithm, significantly impacting the implementation performance of AES chips. To design a high-performance S-box, a segmented optimization... The SubBytes (S-box) transformation is the most crucial operation in the AES algorithm, significantly impacting the implementation performance of AES chips. To design a high-performance S-box, a segmented optimization implementation of the S-box is proposed based on the composite field inverse operation in this paper. This proposed S-box implementation is modeled using Verilog language and synthesized using Design Complier software under the premise of ensuring the correctness of the simulation result. The synthesis results show that, compared to several current S-box implementation schemes, the proposed implementation of the S-box significantly reduces the area overhead and critical path delay, then gets higher hardware efficiency. This provides strong support for realizing efficient and compact S-box ASIC designs. 展开更多
关键词 Advanced Encryption standard (AEs) s-BOX Tower Field Hardware Implementation Application specific Integration circuit (AsIC)
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基于Simulink的Chua’s Circuit混沌实验的可视化模型及仿真研究 被引量:1
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作者 李凌云 王海军 张敏锐 《实验技术与管理》 CAS 2006年第6期79-82,共4页
以大学物理实验中的Chua’s Circuit混沌实验为例,提出了运用Simulink建立Chua’s Circuit混沌实验可视化模型的方法,并对混沌系统的几种状态进行仿真研究。
关键词 Chua’s circuit 混沌实验 sIMULINK 可视化模型 仿真
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A novel mixed-synchronization phenomenon in coupled Chua's circuits via non-fragile linear control 被引量:3
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作者 王军威 马庆华 曾丽 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第8期113-119,共7页
Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme. In this paper, a non-fragile linear feedback control strategy with multipl... Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme. In this paper, a non-fragile linear feedback control strategy with multiplicative controller gain uncertainties is proposed for realizing the mixed-synchronization of Chua's circuits connected in a drive-response configuration. In particular, in the mixed-synchronization regime, different state variables of the response system can evolve into complete synchronization, anti-synchronization and even amplitude death simultaneously with the drive variables for an appropriate choice of scaling matrix. Using Lyapunov stability theory, we derive some sufficient criteria for achieving global mixed-synchronization. It is shown that the desired non-fragile state feedback controller can be constructed by solving a set of linear matrix inequalities (LMIs). Numerical simulations are also provided to demonstrate the effectiveness of the proposed control approach. 展开更多
关键词 mix-synchronization Chua's circuit non-fragile control Lyapunov stability linear ma-trix inequality
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Science Letters:The Moore’s Law for photonic integrated circuits 被引量:2
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作者 THYLEN L. HE Sailing +1 位作者 WOSINSKI L. DAI Daoxin 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第12期1961-1967,共7页
We formulate a “Moore’s law” for photonic integrated circuits (PICs) and their spatial integration density using two methods. One is decomposing the integrated photonics devices of diverse types into equivalent bas... We formulate a “Moore’s law” for photonic integrated circuits (PICs) and their spatial integration density using two methods. One is decomposing the integrated photonics devices of diverse types into equivalent basic elements, which makes a comparison with the generic elements of electronic integrated circuits more meaningful. The other is making a complex compo- nent equivalent to a series of basic elements of the same functionality, which is used to calculate the integration density for func- tional components realized with different structures. The results serve as a benchmark of the evolution of PICs and we can con- clude that the density of integration measured in this way roughly increases by a factor of 2 per year. The prospects for a continued increase of spatial integration density are discussed. 展开更多
关键词 Moore's Law Photonic integrated circuit (PIC) Photonic lightwave circuit (PLC) Photonic integration density Photonic filters Photonic multiplexing
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Synchronization of Modified Chua's Circuit with x|x| Function 被引量:1
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作者 TANG Fang WANG Ling 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第2X期303-306,共4页
This paper considers the chaos synchronization of the modified Chua 's circuit with x|x| function. We firstly show that a couple of the modified Chua systems with different parameters and initial conditions can be... This paper considers the chaos synchronization of the modified Chua 's circuit with x|x| function. We firstly show that a couple of the modified Chua systems with different parameters and initial conditions can be synchronized using active control when the values of parameters both in drive system and response system are known aforehand.Furthermore, based on Lyapunov stability theory we propose an adaptive active control approach to make the states of two identical Chua systems with unknown constant parameters asymptotically synchronized. Moreover the designed controller is independent of those unknown parameters. Numerical simulations are given to validate the proposed synchronization approach. 展开更多
关键词 chaos synchronization modified Chua's circuit active control adaptive active control
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Reduction of signal reflection along through silicon via channel in high-speed three-dimensional integration circuit 被引量:1
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作者 刘晓贤 朱樟明 +2 位作者 杨银堂 王凤娟 丁瑞雪 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第3期583-590,共8页
The through silicon via (TSV) technology has proven to be the critical enabler to realize a three-dimensional (3D) gigscale system with higher performance but shorter interconnect length. However, the received dig... The through silicon via (TSV) technology has proven to be the critical enabler to realize a three-dimensional (3D) gigscale system with higher performance but shorter interconnect length. However, the received digital signal after trans- mission through a TSV channel, composed of redistribution layers (RDLs), TSVs, and bumps, is degraded at a high data-rate due to the non-idealities of the channel. We propose the Chebyshev multisection transformers to reduce the signal reflec- tion of TSV channel when operating frequency goes up to 20 GHz, by which signal reflection coefficient ($11) and signal transmission coefficient ($21) are improved remarkably by 150% and 73.3%, respectively. Both the time delay and power dissipation are also reduced by 4% and 13.3%, respectively. The resistance-inductance-conductance-capacitance (RLGC) elements of the TSV channel are iterated from scattering (S)-parameters, and the proposed method of weakening the signal reflection is verified using high frequency simulator structure (HFSS) simulation software by Ansoft. 展开更多
关键词 three-dimensional integrated circuit through silicon via channel signal reflection s-PARAMETERs
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引入射频诱导效应的BCT PD-SOI MOSFET建模技术研究 被引量:1
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作者 黎莹 王军 《电子元件与材料》 CAS 北大核心 2023年第3期347-353,共7页
为了精确模拟高漏源电压(V_(DS))条件下体接触(Body Contact,BCT)部分耗尽型(Partial Depletion,PD)绝缘体上硅(Silicon-on-Insulator,SOI)MOSFET器件的异常射频诱导效应,建立了一个基于碰撞电离和寄生BJT机理的RL网络模型。首先分析了S... 为了精确模拟高漏源电压(V_(DS))条件下体接触(Body Contact,BCT)部分耗尽型(Partial Depletion,PD)绝缘体上硅(Silicon-on-Insulator,SOI)MOSFET器件的异常射频诱导效应,建立了一个基于碰撞电离和寄生BJT机理的RL网络模型。首先分析了SCBE模型的体区输出导纳参数,并利用该参数的解析式推导出一种电阻与电感串联的网络拓扑;然后基于直接提取法准确提取RL网络模型的参数;最后,通过仿真得出S21、S22参数分别在史密斯圆图的下半圆和上半圆按顺时针旋转的现象,同时在0.01~20 GHz范围内模型模拟的S参数与实测的S参数的相对误差为2.1%,验证了RL网络模型的有效性和准确性。 展开更多
关键词 BCT PD-sOI MOsFET 小信号等效电路 射频诱导效应 s参数
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Controllability of fractional-order Chua's circuit
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作者 张浩 陈帝伊 +1 位作者 周坤 王一琛 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第3期26-30,共5页
The ultimate proof of our understanding of nature and engineering systems is reflected in our ability to control them.Since fractional calculus is more universal, we bring attention to the controllability of fractiona... The ultimate proof of our understanding of nature and engineering systems is reflected in our ability to control them.Since fractional calculus is more universal, we bring attention to the controllability of fractional order systems. First,we extend the conventional controllability theorem to the fractional domain. Strictly mathematical analysis and proof are presented. Because Chua's circuit is a typical representative of nonlinear circuits, we study the controllability of the fractional order Chua's circuit in detail using the presented theorem. Numerical simulations and theoretical analysis are both presented, which are in agreement with each other. 展开更多
关键词 CONTROLLABILITY Chua's circuit fractional order circuit
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直通道PCHE内S-CO_(2)与铅铋合金耦合换热特性数值分析 被引量:1
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作者 刘凯 彭军 +3 位作者 赵富龙 董显敏 田瑞峰 谭思超 《哈尔滨工程大学学报》 EI CAS CSCD 北大核心 2023年第12期2103-2111,共9页
针对超临界二氧化碳(S-CO_(2))与液态铅铋合金在印刷电路板换热器内耦合换热问题,本文建立了“1对2型”直通道印刷电路板换热器换热单元三维模型。采用数值模拟方法对S-CO_(2)与液态铅铋合金耦合换热特性进行了研究。结果表明:冷侧S-CO_... 针对超临界二氧化碳(S-CO_(2))与液态铅铋合金在印刷电路板换热器内耦合换热问题,本文建立了“1对2型”直通道印刷电路板换热器换热单元三维模型。采用数值模拟方法对S-CO_(2)与液态铅铋合金耦合换热特性进行了研究。结果表明:冷侧S-CO_(2)对流换热热阻远大于热侧液态铅铋合金热阻,即印刷电路板换热器整体换热更受制于S-CO_(2)的影响,且S-CO_(2)侧的换热强度决定了整体换热的下限。改变S-CO_(2)侧入口质量流速比改变液态铅铋合金侧入口质量流速对印刷电路板换热器换热器单元功率影响程度更大。S-CO_(2)侧入口质量流速每增加1 kg/s,换热功率增加335.77 kW。本文研究结果可为后续液态铅铋合金与S-CO_(2)耦合换热研究和印刷电路板换热器设计提供参考。 展开更多
关键词 超临界CO_(2) 铅铋合金 印刷电路板 换热器 直通道 耦合换热特性 超临界流体 数值分析
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延迟焦化装置密闭除焦系统S-CCHS技术应用总结 被引量:2
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作者 温传忠 杜亮 《炼油技术与工程》 CAS 2023年第8期28-32,共5页
安全环保型延迟焦化密闭除焦、输送及存储成套技术(S-CCHS)的投用,实现了石油焦处理全过程密闭清洁化操作。运行过程暴露出冷切焦水系统中焦粉含量明显增加、各输送带尾部溜料、输送带清扫效果不佳、装车过程中产生焦粉弥漫、设备故障... 安全环保型延迟焦化密闭除焦、输送及存储成套技术(S-CCHS)的投用,实现了石油焦处理全过程密闭清洁化操作。运行过程暴露出冷切焦水系统中焦粉含量明显增加、各输送带尾部溜料、输送带清扫效果不佳、装车过程中产生焦粉弥漫、设备故障率高等问题,影响装置的安全平稳运行,对环保产生不利影响。通过优化冷切焦水系统流程,系统中焦粉质量浓度从200 mg/L降至20~40 mg/L,下降明显;通过对传输带、定量料仓的全密闭改造,从根本上解决了焦粉向大气中弥漫的问题;通过对高故障率设备进行更新并制定预防性维修计划,有效降低了密闭除焦现场设备故障率。为延迟焦化装置密闭除焦同类技术的应用提供了参考。 展开更多
关键词 延迟焦化装置 密闭除焦系统 s-CCHs 水路系统 焦路系统 气路系统 耐磨水泵 粉焦含量 冷切焦水系统
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DESIGN METHOD OF CHUA'S CIRCUIT FOR SPECIFIED SPECTRUM DISTRIBUTION
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作者 Ran Lixin Chen Kangsheng(Dept. of Information & Electronic Engineering, Zhejiang Univ., Hangzhou 310027) 《Journal of Electronics(China)》 1999年第2期187-192,共6页
Based on the α-β bifurcation curves and the special characteristics of chaotic spectrum of chua’s circuit, this paper presents here a method for designing a Chua’s circuit which approximately satisfy specified spe... Based on the α-β bifurcation curves and the special characteristics of chaotic spectrum of chua’s circuit, this paper presents here a method for designing a Chua’s circuit which approximately satisfy specified spectrum distribution range. 展开更多
关键词 CHAOTIC circuit Chua’s circuit sPECTRUM DIsTRIBUTION
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Non-smooth bifurcations in a double-scroll circuit with periodic excitation
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作者 张银 毕勤胜 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第1期186-193,共8页
The fast-slow effect can be observed in a typical non-smooth electric circuit with order gap between the natural frequency and the excitation frequency. Numerical simulations are employed to show complicated behaviour... The fast-slow effect can be observed in a typical non-smooth electric circuit with order gap between the natural frequency and the excitation frequency. Numerical simulations are employed to show complicated behaviours, especially different types of busting phenomena. The bifurcation mechanism for the bursting solutions is analysed by assuming the forms of the solutions and introducing the generalized Jacobian matrix at the non-smooth boundaries, which can also be used to account for the evolution of the complicated structures of the phase portraits with the variation of the parameter. Period-adding bifurcation has been explored through the computation of the eigenvalues related to the solutions. At the non-smooth boundaries the so-called 'single crossing bifurcation' can occur, corresponding to the case where the eigenvalues jump only once across the imaginary axis, which leads the periodic burster to have a quasi-periodic oscillation. 展开更多
关键词 Matsumoto's circuit non-smooth bifurcation fast-slow effect BURsTING
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Stability and boundary equilibrium bifurcations of modified Chua's circuit with smooth degree of 3
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作者 Shihui FU Xiangying MENG Qishao LU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2015年第12期1639-1650,共12页
Chua's circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua's circuit system with the smooth deg... Chua's circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua's circuit system with the smooth degree of 3 are studied. The parametric areas of stability are specified in detail. It is found that the bifurcation graphs of the su- percritical and irregular pitchfork bifurcations are similar to those of the piecewise-smooth continuous (PWSC) systems caused by piecewise smoothness. However, the bifurcation graph of the supercritical Hopf bifurcation is similar to those of smooth systems. There- fore, the boundary equilibrium bifurcations of the non-smooth systems with the smooth degree of 3 should receive more attention due to their special features. 展开更多
关键词 modified Chua's circuit boundary equilibrium point sTABILITY BIFURCATION
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Study on eigenvalue space of hyperchaotic canonical four-dimensional Chua's circuit
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作者 李冠林 陈希有 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第3期137-144,共8页
The eigenvalue space of the canonical four-dimensional Chua's circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parame... The eigenvalue space of the canonical four-dimensional Chua's circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parameters and the eigenvalues of the system are established, and therefore all the circuit parameters can be determined explicitly by any given set of eigenvalues. Then, the eigenvalue space of the circuit is investigated in two cases by the nonlinear elements used. According to the types of the eigenvalues, some novel hyperchaotic attractors are presented. Further, the dynamic behaviours of the circuit are studied by the bifurcation diagrams and the Lyapunov spectra of the eigenvalues. 展开更多
关键词 four-dimensional Chua's circuit eigenvalue space HYPERCHAOs
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Synchronising chaotic Chua's circuit using switching feedback control based on piecewise quadratic Lyapunov functions
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作者 张洪斌 夏建伟 +1 位作者 于永斌 党创寅 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第3期122-129,共8页
This paper investigates the chaos synchronisation between two coupled chaotic Chua's circuits. The sufficient condition presented by linear matrix inequalities (LMIs) of global asymptotic synchronisation is attaine... This paper investigates the chaos synchronisation between two coupled chaotic Chua's circuits. The sufficient condition presented by linear matrix inequalities (LMIs) of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions (pwLDIs) model of synchronisation error dynamics, then we design a switching (piecewise-linear) feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results. 展开更多
关键词 CHAOs Chua's circuit piecewise quadratic Lyapunov functions synchronisation
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