After years of development, chaotic circuits have possessed many different mathematic forms and multiple realization methods. However, in most of the existing chaotic systems, the nonlinear units are composed of the product terms. In this paper, in order to obtain a chaotic oscillator with higher nonlinearity and complexity to meet the needs of utilization, we discuss a novel chaotic system whose nonlinear term is realized by an exponential term. The new exponential chaotic oscillator is constructed by adding an exponential term to the classical Lu system. To further investigate the dynamic characteristics of the oscillator, classical theoretical analyses have been performed, such as phase diagrams, equilibrium points, stabilities of the system, Poincare mappings, Lyapunov exponent spectrums, and bifurcation diagrams. Then through the National Institute of Standards and Technology ( NIST ) statistical test, it is proved that the chaotic sequence generated by the exponential chaotic oscillator is more random than that produced by the Lu system. In order to further verify the practicability of this chaotic oscillator, by applying the improved modular design method, the system equivalent circuit has been realized and proved by the Multisim simulation. The theoretical analysis and the Multisim simulation results are in good agreement.

中文翻译：

---

指数混沌振荡器的设计及其动力学分析

经过多年的发展，混沌电路具有许多不同的数学形式和多种实现方法。但是，在大多数现有的混沌系统中，非线性单元由乘积项组成。为了获得具有更高非线性度和复杂度的混沌振荡器以满足应用需求，本文讨论了一种新型的非线性系统，其非线性项可以通过指数项来实现。通过在经典Lu系统中添加一个指数项来构造新的指数混沌振荡器。为了进一步研究振荡器的动态特性，已经进行了经典的理论分析，例如相图，平衡点，系统稳定性，庞加莱映射，Lyapunov指数谱和分叉图。然后通过美国国家标准技术研究院（NIST）的统计测试，证明了指数混沌振荡器产生的混沌序列比Lu系统产生的混沌序列更随机。为了进一步验证该混沌振荡器的实用性，通过采用改进的模块化设计方法，已经实现了系统等效电路，并通过Multisim仿真对其进行了证明。理论分析与Multisim仿真结果吻合良好。通过Multisim仿真实现并证明了系统等效电路。理论分析与Multisim仿真结果吻合良好。通过Multisim仿真实现并证明了系统等效电路。理论分析与Multisim仿真结果吻合良好。