Reversals of period doubling, coexisting multiple attractors, and offset boosting in a novel memristive diode bridge-based hyperjerk circuit
Reversals of period doubling, coexisting multiple attractors, and offset boosting in a novel memristive diode bridge-based hyperjerk circuit
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DOI：
10.1007/s10470-018-1372-5
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发表时间：
2018-12
影响因子：
1.4
通讯作者：
J. Kengne;G. D. Leutcho;Adelaide Nicole Kengnou Telem
中科院分区：
文献类型：
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作者：
J. Kengne;G. D. Leutcho;Adelaide Nicole Kengnou Telem
本文提出了一种新的基于记忆二极管桥式RC超急变电路。这种新的记忆超急流振荡器(MHO)是从自治的四维超急动电路中获得的(Leutcho等人。在混沌孤子中)，通过用一阶记忆二极管电桥取代非线性分量(由两个反平行二极管形成)。该电路由一个具有光滑非线性的五阶连续时间自治(优雅的)超急动系统描述。通过平衡点和稳定性、相图、分岔图和双参数Lyapunov指数图研究了系统的动力学。模型的数值分析揭示了一些有趣的行为，如倍周期、混沌、偏置提升、对称性恢复危机、反单调性(即同时产生和破坏周期轨道)以及几个共存的分叉。本文所考虑的新的MHO最吸引人的特征之一是，对于某些合适的系统参数集，根据初始条件的选择，存在多个共存的吸引子(例如，两个、三个、四个、五个、六个、七个或九个吸引子共存)。相应地，计算与每个共存吸引子相关的初始条件的分布，以突出不同的吸引盆地。进行了实验室实验测量，验证了理论分析的正确性。
In this paper, a new memristive diode bridge-based RC hyperjerk circuit is proposed. This new memristive hyperjerk oscillator (MHO) is obtained from the autonomous 4-D hyperjerk circuit (Leutcho et al. in Chaos Solitons Fractals 107:67–87, 2018) by replacing the nonlinear component (formed by two antiparallel diodes) with a first order memristive diode bridge. The circuit is described by a fifth-order continuous time autonomous (‘elegant’) hyperjerk system with smooth nonlinearities. The dynamics of the system is investigated in terms of equilibrium points and stability, phase portraits, bifurcation diagrams and two-parameter Lyapunov exponents diagrams. The numerical analysis of the model reveals interesting behaviors such as period-doubling, chaos, offset boosting, symmetry recovering crisis, antimonotonicity (i.e. concurrent creation and destruction of periodic orbits) and several coexisting bifurcations as well. One of the most attractive features of the new MHO considered in this work is the presence of several coexisting attractors (e.g. coexistence of two, three, four, five, six, seven, or nine attractors) for some suitable sets of system parameters, depending on the choice of initial conditions. Accordingly, the distribution of initial conditions related to each coexisting attractor is computed to highlight different basins of attraction. Laboratory experimental measurements are carried out to verify the theoretical analysis.