Memristor, as a nonlinear element, provides many advantages thanks to its superior properties to design different chaotic circuits. Thus, a novel four-dimensional double-scroll chaotic system with line equilibria as well as two unstable equilibria based on the flux-memristor model is proposed in this paper. The effects of initial values and parameters on the dynamic characteristics of the system are studied in detail by means of phase diagrams, Lyapunov exponent spectrums, bifurcation diagrams, two-parameter bifurcation diagrams and basins of attraction. Besides, a series of complex phenomena in the system, such as sustained chaos, bistability, transient chaos and coexisting attractors are observed, proving that the chaotic system has rich dynamic characteristics. Also, spectral entropy (SE) complexity algorithm and C0 complexity algorithm based on structure complexity are adopted to analyze the complexity of the system. Additionally, PSPICE circuit simulation and Micro-Controller Unit (MCU) hardware experiment are carried out to verify the correctness of theoretical analysis and numerical simulation. Finally, the pulse chaos synchronization is achieved from the perspective of maximum Lyapunov exponent, and numerical simulations demonstrate the occurrence of the proposed system and practicability of the pulse synchronization control.

中文翻译：

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一种新的基于忆阻器的具有线平衡的混沌系统及其复杂动力学

忆阻器作为一种非线性元件，由于其优异的特性可以设计不同的混沌电路，因此具有许多优势。因此，本文提出了一种基于通量忆阻器模型的具有线平衡和两个不稳定平衡的新型四维双涡旋混沌系统。通过相图、李雅普诺夫指数谱、分岔图、二参数分岔图和吸引盆等方法，详细研究了初始值和参数对系统动态特性的影响。此外，还观察到了系统中的持续混沌、双稳态、瞬态混沌和吸引子共存等一系列复杂现象，证明了混沌系统具有丰富的动态特性。此外，谱熵 (SE) 复杂度算法和C0采用基于结构复杂度的复杂度算法来分析系统的复杂度。此外，还进行了PSPICE电路仿真和微控制器单元（MCU）硬件实验，验证了理论分析和数值仿真的正确性。最后，从最大李雅普诺夫指数的角度实现了脉冲混沌同步，数值模拟证明了所提系统的出现和脉冲同步控制的实用性。