Ding Lina, Xuan Mengtian
School of Electronics and Information Engineering, Heilongjiang University of Science and Technology, Harbin 150022, China.
Entropy (Basel). 2025 Apr 29;27(5):481. doi: 10.3390/e27050481.
In order to further explore the complex dynamical behavior involved in super-multistability, a new five-dimensional memristive chaotic system was obtained by using a magnetically controlled memristor to construct a four-dimensional equation on the basis of a three-dimensional chaotic system, adding a five-dimensional equation and selecting parameter y as the control term. Firstly, the multistability of the system was analyzed by using a Lyapunov exponential diagram, a bifurcation diagram and a phase portrait; the experimental results show that the system has parameter-related periodic chaotic alternating characteristics, symmetric attractors and transient chaotic characteristics, and it also has the characteristics of homogeneous multistability, heterogeneous multistability and super-multistability, which depend on the initial memristive values. Secondly, two offset constants g and h were added to the linear state variables, which were used as controllers of the attractors in the z and w directions, respectively, and the influences of the bidirectional offset increments on the system were analyzed. The complexity of the system was analyzed; the higher the complexity of the system, the larger the values of the complexity, and the darker the colors of the spectrogram. The five-dimensional memristive chaotic system was simulated using Multisim to verify the feasibility of the new system. Finally, an adaptive synchronization controller was designed using the method of adaptive synchronization; then, synchronization of the drive system and the response system was realized by changing the positive gain constant k, which achieved encryption and decryption of sinusoidal signals based on chaotic synchronization.
为了进一步探究超多重稳定性中涉及的复杂动力学行为，在一个三维混沌系统的基础上，通过使用磁控忆阻器构建一个四维方程，添加一个五维方程并选择参数y作为控制项，得到了一个新的五维忆阻混沌系统。首先，利用李雅普诺夫指数图、分岔图和相图分析了系统的多重稳定性；实验结果表明，该系统具有与参数相关的周期混沌交替特性、对称吸引子和瞬态混沌特性，并且还具有均匀多重稳定性、非均匀多重稳定性和超多重稳定性的特征，这取决于初始忆阻值。其次，在线性状态变量中添加了两个偏移常数g和h，它们分别用作z和w方向上吸引子的控制器，并分析了双向偏移增量对系统的影响。分析了系统的复杂性；系统的复杂性越高，复杂性值越大，频谱图的颜色越深。使用Multisim对五维忆阻混沌系统进行了仿真，以验证新系统的可行性。最后，采用自适应同步方法设计了一个自适应同步控制器；然后，通过改变正增益常数k实现了驱动系统和响应系统的同步，基于混沌同步实现了正弦信号的加密和解密。
