基于Chua电路的四维超混沌忆阻电路

摘要

近年来，忆阻混沌电路受到国内外学者的广泛关注，然而目前四维忆阻系统往往只存在普通混沌(仅有一个正Lyapunov指数)。本文通过用忆阻替换Chua电路中电阻的新途径，得出一个简单的四维忆阻电路。与仅含有限个孤立不稳定平衡点的大多已知系统不同，本系统存在无穷多个稳定和不稳定平衡点。研究发现该系统存在着极限环、混沌、超混沌等丰富的复杂行为。通过进一步数值分析和电路仿真实验，证实了超混沌吸引子的存在，从而解决了关于四维忆阻电路是否存在超混沌的疑问。%Recently, there has been a growing interest in chaotic memristive circuits. However, four-dimensional (4D) memris-tive system often can only exhibit common chaos with only one positive Lyapunov exponent. By replacing the resistor of Chua’s circuit with a memristor, we propose a new simple 4D memristive circuit in this paper. A major difference between our proposed system and the known chaotic or hyperchaotic system is that our modified system has infinitely many stable and unstable equilibria. We show that the system can exhibit rich complex dynamic behaviors, such as limit cycles, chaos and hyperchaos. Further numerical study and circuit simulation verify the existence of a hyperchaotic attractor in the memristive circuit, which gives a positive answer about whether there exists hyperchaos in 4D memristive systems.