忆阻开关混沌电路及其吸引子共存现象研究

为了研究忆阻开关电路的动力学行为,该文提出一种具有多吸引子共存现象的忆阻开关混沌电路。在该电路中存在多吸引子分岔,当系统中发生边界碰撞之后,系统中将产生不同的吸引子共存现象。其中包括单周期极限环与混沌吸引子共存,不同的混沌吸引子共存,对称的2周期极限环共存现象,以及对称的2周期极限环与5周期极限环共存现象等。该文通过相图、分岔图等数值仿真,分析了该电路的动力学行为,并利用PSIM电路仿真验证了其电路的可行性,对开关电路中多吸引子共存现象和混沌应用的研究具有重要意义。     

一种新型双忆阻混沌系统动力学及其电路实现研究

在经典的蔡氏混沌电路基础上,引入三次非线性磁控忆阻模型,利用一个磁控忆阻模型和一个荷控忆阻模型,外加一个负电导替换变形蔡氏电路中的蔡氏二极管,设计了一个五阶混沌电路,用常规的方法研究系统的基本动力学特性。通过数值仿真结果表明电路在参数变化情况下能产生Hopf分岔和反倍周期分岔两种分岔行为,并能产生双涡卷、单涡卷、极限环、同宿轨等不同轨道,出现了双单摆运动。观察混沌吸引子推广到功率与能量信号,观察到蝴蝶翅膀重叠的奇异吸引子。通过改变初始值,能产生共存吸引子和周期极限环共存现象。为了验证电路的混沌行为,将对设计的电路进行了PSpice仿真,电路仿真结果验证了理论分析的正确性。     

新型多翼统一混沌系统

通过引入多个线性状态反馈控制项和非线性状态反馈控制项,提出了一个新型多翼统一混沌系统。在不同的系统参数下均能产生关于原点对称的真实四翼混沌吸引子,还能产生蝴蝶吸引子、蝙蝠形吸引子和新型多翼混沌吸引子。采用常规的动力学分析方法研究了产生新型多翼混沌吸引子系统的基本动力学特性,例如相图、耗散性分析、李雅普诺夫指数谱和分岔图。结果表明系统可以产生丰富的混沌行为,该新型多翼混沌吸引子可以随参数的变化实现关于x轴对称的双翼混沌吸引子和关于原点对称的真实四翼混沌吸引子。     

峰值电压反馈Superbuck变换器中分岔与混沌的实验研究

该文针对太阳能光伏发电系统中一种重要的拓扑结构 Superbuck 变换器进行非线性动力学研究。根据变换器的状态方程,采用频闪映射方法得到变换器的离散映射模型,然后以参考电压为分岔参数得到电感电流的分岔图。最后通过建立实验电路来研究变换器的非线性动力学行为,验证系统从稳定到倍周期分岔直至混沌态的演化过程,同时通过分析电感电流的功率谱图,证明应用混沌技术可以有效地降低系统的电磁干扰(EMI)。     

三维非谐势阱中BEC混沌动力学研究

玻色一爱园斯坦凝聚（BEC）是一种新的物质形态,一个宏观量子系统。本文在平均场理论和双模近似的框架下,推导出研究玻色一爱因斯坦凝聚体动力学行为及其性质的数学模型Gross—Pitaevskii方程,用数值方法通过Fortran语言和Madab程序模拟研究了该系统基态波函数和化学势随非线性项的变化,并对其混沌特征和吸引子等非线性动力学参数做了分析,并从模拟数据发现了在临界值处直接由周期态进入混沌态,没有经历准周期行为,而且状态随初始条件的变化而变化,从瞬态混沌到定态混沌经过了一系列的分岔的现象。     

一个具有无限多吸引子共存的新混沌系统的动力学分析及其电路实现

提出了一个新的具有超多稳定性的三维连续自治混沌系统,该系统仅有2个非线性项.对系统的耗散性、平衡点的稳定性进行了定量分析,并利用分岔图、Lyapunov指数、彭加莱截面和吸引子相图分析了系统参数以及初值对其动力学行为的影响.在参数固定的情况下,分析初值变化的分岔图,得到了无限多种共存吸引子.通过采用模拟开关电子元件设计实现了该系统,同时运用Multisim软件仿真了该系统的混沌电路.结论证明电路仿真与数值仿真结果一致.     

一个新的超混沌系统及其电路实现

通过对一个光滑三维二次混沌系统上引入一个新的状态反馈控制器,构造出一个新的四维超混沌系统。详细地分析了该系统平衡点的性质、超混沌吸引子相图、Lyapunov指数和分岔图等基本动力学特性。数值模拟结果表明,新的四维系统能随着参数变化呈现出周期态、拟周期态、混沌态和超混沌态等丰富的动力学行为。最后设计了硬件电路实验,也很好的证实了相关结果。     

基于双曲函数的双忆阻器混沌电路多稳态特性分析

基于经典蔡氏混沌振荡电路,引入一种双曲余弦函数的新型磁控忆阻器模型,设计含有两个双曲余弦忆阻器的混沌电路系统,讨论了系统平衡点集面的稳定区间.选择不同的忆阻初始值进行数值仿真,通过分岔图与Lyapunov指数谱研究双曲忆阻混沌系统的多稳态特性.结果表明,含双曲函数的双忆阻混沌电路具有复杂的动力学行为,运动轨迹不仅依赖于电路参数,还受电路的初始状态影响,由此产生了不同拓扑结构的混沌吸引子与不同周期运动的多稳态隐藏吸引子共存现象.     

一类电路系统的分岔分析及超混沌控制研究

为了揭示电路系统丰富的非线性动力学行为,提高电路系统的稳定性,避免混沌或超混沌电路对元器件的危害,针对一类电路系统模型,应用现代数学中的微分方程理论和非线性动力学的方法,分析了系统发生分岔的条件,并通过数值分析验证了该理论结果。研究发现系统在一定参数条件下存在内衣马克-沙克分岔和倍周期分岔,随着参数的变化系统演化为混沌和超混沌。针对目前超混沌控制方法的研究较少,而且控制的周期轨道多是低周期轨道,提出一种节约能量并能将系统控制到高倍周期和概周期的方法,为研究许多现实离散系统模型提供了一种新的方法,对于研究电路系统提供了一条新的思路,因而具有一定的理论意义和实用价值。     

分数阶忆阻退化Jerk系统的特性分析与DSP实现

为了探究分数阶形式下该类系统的动力学特性,该文将分数阶微积分引入到忆阻退化Jerk系统中,增加了一个自由度,提升了系统性能。通过相图、分岔图、李雅普诺夫指数谱、复杂度混沌图等分析了系统的动力学特性,并采用DSP技术,实现了该系统的数字电路。研究结果表明,系统拓展到分数阶后有两种不同的单涡卷吸引子,系统随初值变化呈现倍周期分岔路径,在某些特定初值处系统演化路径出现跃变。系统具有无限多个吸引子共存。     

Coexistence of infinite attractors in a fractional-order chaotic system with two nonlinear functions and its DSP implementation

In this paper, a new five-dimensional fractional-order chaotic system based on two nonlinear functions is constructed. The rich dynamical behaviors of the system are analyzed by phase diagram, bifurcation diagram and Lyapunov exponents spectrum. In addition, the complexity of the fractional-order system is analyzed through Spectral Entropy (SE) and Permutation Entropy (PE) algorithms. Meanwhile the phenomenon of coexisting infinite attractors is analyzed. Of particular concern is that the phenomenon of multi-state transition and intermittent oscillation chaos is found in this new chaotic system. Furthermore, the system is implemented on the DSP platform. To the best of the knowledge, these rich dynamical characteristics and complicated phenomena are of great reference value in chaotic image encryption and other fields.     

A new multi-scroll Chua’s circuit with composite hyperbolic tangent-cubic nonlinearity: Complex dynamics,Hardware implementation and Image encryption application

In this paper, a new method for generating multi-scroll chaotic attractors via constructing a compound hyperbolic tangent-cubic nonlinear function in canonical Chua’s circuit is presented. The basic dynamic characteristics of the system are analyzed, including equilibrium points, bifurcation diagrams, Lyapunov exponents, phase portraits, time-domain diagrams and attractive basins. What is surprising is that the proposed multi-scroll Chua’s circuit also exhibits rich dynamic behaviors like coexisting multiple attractors, transient period, intermittent chaos and offset boosting. In addition, we put forward the application of the system in chaotic image encryption, and analyzed some security performance evaluation indexes to show that the new Chua’s chaotic cipher system has high security and reliable encryption performance. Finally, the hardware design and experiments of the chaotic digital circuits and image encryption are carried out. Both numerical simulation and FPGA experimental results verify the feasibility and usability of the proposed new multi-scroll Chua’s system.     

PWM型开关电容DC-DC变换器的 非线性动力学行为研究

建立了PWM型二阶开关电容DC-DC变换器的二维离散映射模型,用非线性动力学理论分析了映射模型定点的稳定情况.以电压反馈系数为参数,通过数值计算描绘了系统动态演化的分岔图和最大Lyapunov指数变化曲线.以二阶串并电容组合开关电容DC-DC变换器为例,用PSPICE软件对其进行模拟仿真,得到了变换器的混沌吸引子.理论分析、数值计算和模拟仿真保持了一致.     

Analysis of Spatiotemporal Patterns in an Infinite-Dimensional Electromagnetic System

An infinite-dimensional electromagnetic system is proposed as a practical model for analyzing the spatiotemporal chaos. The system consists of a linear lossless transmission line connected to a p-n-junction diode in series with a DC bias voltage source at one end and to an active linear resistor at the other end. The temporal dynamics of the backward-traveling voltage wave is investigated by using a corresponding one-dimensional map, and the effects of the serial dc bias voltage source on the dynamics of the system are particularly studied here. Numerical results are presented to show that the spatiotemporal nonlinear oscillation of the voltages along the lossless transmission line is the oscillation of isotropism with respect to space and time, and spatial intermittency and chaos exist in this infinite-dimensional electromagnetic system. Several spatiotemporal patterns of the voltages are also observed.     

Coexistence of multiple bifurcation modes in memristive diode-bridge-based canonical Chua’s circuit

Based on a memristive diode bridge cascaded with series resistor and inductor filter, a modified memristive canonical Chua’s circuit is presented in this paper. With the modelling of the memristive circuit, a normalised system model is built. Stability analyses of the equilibrium points are performed and bifurcation behaviours are investigated by numerical simulations and hardware experiments. Most extraordinary in the memristive circuit is that within a parameter region, coexisting phenomenon of multiple bifurcation modes is emerged under six sets of different initial values, resulting in the coexistence of four sets of topologically different and disconnected attractors. These coexisting attractors are easily captured by repeatedly switching on and off the circuit power supplies, which well verify the numerical simulations.     

电压模式 Buck变换器典型工作状态分析

电压控制型Buck变换器是典型的非线性电路系统。根据DC-DC Buck变换器的工作特性,建立了研究其非线性现象的仿真模型,分析了Buck变换器的分岔稳定性和混沌化特性,揭示了以输入电压和电感作为分叉参数的混沌现象及系统输出特性;从时域角度分析参考电压波形与输出电压波形交点的变化对变换器工作状态的影响,在相图中得到系统由稳定到混沌的演化过程,并验证了该模型的合理性和可行性。该研究方法也为其他模式DC-DC变换器的分岔与混沌现象提供理论和实验基础。     

Novel unified chaotic system with multi-parameter invariable Lyapunov exponent spectrum

Based on the traditional Qi chaotic system,a novel unified chaotic system with the complex chaotic characteristics was constructed by adding the control parameters and modifying the nonlinear terms.Firstly,basic dynamical characteristics of chaotic system were analyzed,and phase portrait,time domain waveform diagram,Poincare mapping and power spectrum diagram were numerically simulated.Secondly,system parameters influence on chaotic system was discussed through Lyapunov exponent spectrum,bifurcation diagrams and chaotic signal amplitude.It was found that the unified chaotic system can generate the four new types of two-wing chaotic attractors with the multi-parameter invariable Lyapunov exponent spectrum characteristics.Meanwhile,there exist the functions of the global and local nonlinear amplitude modulation parameters.Thirdly,taking the first chaotic attractor of system as an example by introducing the two new types of nonlinear functions,the expansion of grid multi-wing attractor was realized.Finally,the hardware circuit of novel unified chaotic system was constructed.The four new types of chaotic attractors are observed experimentally,which is consistent with numerical simulation results and verified the feasibility of the proposed system.     

Dynamics and circuit of a chaotic system with a curve of equilibrium points

Although chaotic systems have been intensively studied since the 1960s, new systems with mysterious features are still of interest. A novel chaotic system including hyperbolic functions is proposed in this work. Especially, the system has an infinite number of equilibrium points. Dynamics of the system are investigated by using non-linear tools such as phase portrait, bifurcation diagram, and Lyapunov exponent. It is interesting that the system can display coexisting chaotic attractors. An electronic circuit for realising the chaotic system has been implemented. Experimental results show a good agreement with theoretical ones.