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| Abstract: |
| The integer-order memristor based chaotic system with time delay have attracted much attention and has been well discussed .However,the fractional-order system is closer to the real systems. In this paper, a nonlinear time-delay chaotic circuit based on fractional-order memristive system was proposed . Some dynamical properties, including equilibrium points, stability, bifurcation and Lyapunov exponent of the oscillator, were investigated in detail by theoretical analyses and simulations. Moreover, the nonlinear phenomena of coexisting bifurcation and attractor was found .The phenomenon shows that the state of this oscilator was highly sensitive to its initial value, which is called coexistent oscillation in this paper. Finally, the results of the system circuit simulation accomplished by Multisim were perfectly consisten with theoretical analysis and numerical simulation. |
| Key words: fractional-order time-delay coexisting attractors coexisting bifurcation circuit simulation. |
| DOI：10.11916/j.issn.1005-9113.18084 |
| Clc Number:O415.5 |
| Fund: |
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| Descriptions in Chinese: |
| 基于整数阶忆阻器的时滞混沌系统已经引起人们的广泛关注和讨论。然而，分数阶系统更接近实际系统。在本文中，我们提出了一种基于分数阶忆阻系统的非线性时滞混沌电路。分析了分数阶忆阻器的频率和电特性。研究了实现分数阶忆阻器的单元电路。通过理论分析和数值仿真，详细研究了振荡器的动力学特性，包括平衡点和稳定性，分岔图和Lyapunov指数。我们还研究了共存分叉和共存吸引子的非线性现象。该现象表明该振荡器的状态对其初始值非常敏感，本文称之为共存振荡。此外，使用改进的Adams-Bashforth-Moulton方法研究数值模拟。最后，我们对该时滞混沌电路进行电路仿真，与理论分析和数值模拟的结果一致。 |
