Meminductive Wein-bridge chaotic oscillator
Meminductive Wein-bridge chaotic oscillator
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DOI：
10.7498/aps.66.020502
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发表时间：
2017-01
影响因子：
1
通讯作者：
Xu Birong;Wang Guangyi
中科院分区：
文献类型：
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作者：
Xu Birong;Wang Guangyi
忆电感器是一种新型的存储器件。因此，对忆感器模型及其在非线性电路中的应用进行深入研究具有重要意义。为此，我们提出了一种新的忆电感器的数学模型，它考虑了内部状态变量的影响，因此将更符合未来的实际忆电感器器件。利用运算放大器、乘法器、电容和电阻等器件，设计了该模型的等效电路，以探讨其特性。该等效电路可用于设计基于忆电感器的应用电路作为忆电感器仿真器。通过仿真实验，研究了这种忆感器在正弦激励下的特性。通过理论分析和仿真，给出了该忆感器模型的电流-磁通（i-φ）、电压-磁通（v-φ）、忆感器内部变量v-ρ和φ-ρ的特性曲线。电流-磁通曲线（i-φ）是一个通过原点的箍缩滞回线。每个子环的边界区域随着频率的变化而变形，并且随着频率的增加，箍缩滞后环的形状趋于直线，表明忆电感器对频率的依赖性。基于忆电感器模型，设计并分析了一种忆电感维恩电桥混沌振荡器。通过理论分析和仿真研究了该系统的平衡点、稳定性、分岔和李雅普诺夫指数等动力学性质。利用李雅普诺夫谱、分岔图和动力学映射，发现系统存在周期、拟周期和混沌状态。此外，该系统还存在一些复杂的非线性现象，如常李雅普诺夫指数谱和混沌信号的非线性调幅。此外，我们还发现了共存分岔和共存吸引子的非线性现象，包括两个不同的混沌吸引子共存和两个不同的周期吸引子共存。这一现象表明，该振子的状态对初值高度敏感，不仅对混沌态，而且对周期态也是如此，本文称之为共存振荡。阐述了现有吸引子的基本原理和潜在应用，它们可用于产生鲁棒伪随机序列或多路伪随机序列。最后，利用所提出的模诱导模型的等效电路，实现了模诱导文氏桥混沌系统的模拟电路。通过示波器显示电路实验结果，验证了振荡器的混沌特性。该振荡器作为一种伪随机信号源，可以产生混沌信号，应用于混沌密码学和保密通信。
A meminductor is a new type of memory device. It is of importance to study meminductor model and its application in nonlinear circuit prospectively. For this purpose, we present a novel mathematical model of meminductor, which considers the effects of internal state variable and therefore will be more consistent with future actual meminductor device. By using several operational amplifiers, multipliers, capacitors and resistors, the equivalent circuit of the model is designed for exploring its characteristics. This equivalent circuit can be employed to design meminductor-based application circuits as a meminductor emulator. By employing simulation experiment, we investigate the characteristics of this meminductor driven by sinusoidal excitation. The characteristic curves of current-flux (i-φ), voltage-flux (v-φ), v-ρ (internal variable of meminductor) and φ-ρ for the meminductor model are given by theoretical analyses and simulations. The curve of current-flux (i-φ) is a pinched hysteretic loop passing through the origin. The area bounding each sub-loop deforms as the frequency varies, and with the increase of frequency, the shape of the pinched hysteretic loop tends to be a straight line, indicating a dependence on frequency for the meminductor. Based on the meminductor model, a meminductive Wien-bridge chaotic oscillator is designed and analyzed. Some dynamical properties, including equilibrium points and the stability, bifurcation and Lyapunov exponent of the oscillator, are investigated in detail by theoretical analyses and simulations. By utilizing Lyapunov spectrum, bifurcation diagram and dynamical map, it is found that the system has periodic, quasi-periodic and chaotic states. Furthermore, there exist some complicated nonlinear phenomena for the system, such as constant Lyapunov exponent spectrum and nonlinear amplitude modulation of chaotic signals. Moreover, we also find the nonlinear phenomena of coexisting bifurcation and coexisting attractors, including coexistence of two different chaotic attractors and coexistence of two different periodic attractors. The phenomenon shows that the state of this oscilator is highly sensitive to its initial valuse, not only for chaotic state but also for periodic state, which is called coexistent oscillation in this paper. The basic mechanism and potential applications of the existing attractors are illustrated, which can be used to generate robust pseudo random sequence, or multiplexed pseudo random sequence. Finally, by using the equivalent circuit of the proposed meminducive model, we realize an analog electronic circuit of the meminductive Wien-bridge chaotic system. The results of circuit experiment are displayed by the oscilloscope, which can verify the chaotic characteristics of the oscillator. The oscillator, as a pseudo random signal source, can be used to generate chaotic signals for the applications in chaotic cryptography and secret communications.