摘要:
采用常见元器件等效实现一个广义忆阻器，进而制作出一个电路特性可靠的非线性电路，有助于忆阻混沌电路的非线性现象的实验展示及其所产生的混沌信号的实际工程应用。基于忆阻二极管桥电路，构建了一种无接地限制的、易物理实现的一阶有源广义忆阻模拟器；由该模拟器并联电容后与RC桥式振荡器线性耦合，实现了一种无电感元件的忆阻混沌电路；建立了无感忆阻混沌电路的动力学模型，开展了相应的耗散性、平衡点、稳定性和动力学行为等分析。结果表明，无感忆阻混沌电路在相空间中存在分布2个不稳定非零鞍焦的耗散区和包含1个不稳定原点鞍点的非耗散区；当元件参数改变时，无感忆阻混沌电路有着共存分岔模式和共存吸引子等非线性行为。研制了实验电路，该电路结构简单、易实际制作，实验测量和数值仿真两者结果一致，验证了理论分析的有效性。
Abstract:
Equivalently implementing a generalized memristor by using common components and then making a nonlinear circuit with a reliable property, are conducive to experimentally exhibit the nonlinear phenomena of the memristive chaotic circuit and show practical applications in generating chaotic signals. Firstly, based on a memristive diode bridge circuit, a new first-order actively generalized memristor emulator is constructed with no grounded restriction and ease to realize. The mathematical model of the emulator is established and its fingerprints are analyzed by the pinched hysteresis loops with different sinusoidal voltage stimuli. The results verified by experimental measurements indicate that the emulator uses only one operational amplifier and nine elementary electronic circuit elements and is an active voltage-controlled generalized memristor. Secondly, by parallelly connecting the proposed emulator to a capacitor and then linearly coupling with an RC bridge oscillator, a memristor based chaotic circuit without any inductance element is constructed. The dynamical model of the inductorless memristive chaotic circuit is established and the phase portraits of the chaotic attractor with typical circuit parameters are obtained numerically. The dissipativity, equilibrium points, and stabilities are derived, which indicate that in the phase space of the inductorless memristive chaotic circuit there exists a dissipative area where are distributed two unstable nonzero saddle-foci and a non-dissipative area containing an unstable origin saddle point. Furthermore, by utilizing the bifurcation diagram, Lyapunov exponent spectra, and phase portraits, the dynamical behaviors of the inductorless memristive chaotic circuit are investigated. Results show that with the evolution of the parameter value of the coupling resistor, the complex nonlinear phenomena of the coexisting bifurcation modes and coexisting attractors under two different initial conditions of the state variables can be found in the inductorless memristive chaotic circuit. Finally, a prototype circuit with the same circuit parameters for numerical simulations is developed, from which it can be seen that the prototype circuit has a simple circuit structure and is inexpensive and easy to practically fabricate with common components. Results of both the experimental measurements and the numerical simulations are consistent, verifying the validity of the theoretical analyses.
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