This paper is devoted to introduce a simplest Lorenz-like chaotic circuit and the calculation of Hamiltonian energy function for the corresponding dimensionless Lorenz-like chaotic system, as well as its applications in weak signal detection and chaotic secure communication. First, a simplest Lorenz-like chaotic circuit composed of three operational amplifiers and two analog multipliers is constructed through simplified circuit design based on a Lorenz chaotic circuit composed of six operational amplifiers and two analog multipliers. Then, the weak signal detection problem of the corresponding Lorenz-like chaotic system is studied by utilizing the extreme sensitivity of chaotic system to initial value in consideration of the inaccuracy of traditional detection methods. Furthermore, the Hamiltonian energy function of the Lorenz-like chaotic system is calculated based on the Helmholtz theorem. In addition, the simplest Lorenz-like chaotic circuit is applied to construct a chaotic secure communication system using the active control synchronization method. Accordingly, the hardware circuits are implemented to prove the effectiveness and feasibility of the simplest Lorenz-like chaotic circuit and the chaotic secure communication circuit.

本文致力于介绍一个最简单的类洛伦兹混沌电路和对应的无量纲类洛伦兹混沌系统的哈密顿能量函数的计算，及其在弱信号检测和混沌保密通信中的应用。首先，在一个由六个运放和两个模拟乘法器组成的洛伦兹混沌电路的基础上，通过简化的电路设计，构造了一个由三个运放和两个模拟乘法器组成的最简单的类洛伦兹混沌电路。然后，考虑到传统检测方法的不准确性，利用混沌系统对初始值的极端敏感性，研究了相应类洛伦兹混沌系统的弱信号检测问题。此外，基于亥姆霍兹定理计算类洛伦兹混沌系统的哈密顿能量函数。此外，应用最简单的类洛伦兹混沌电路，利用主动控制同步方法构建混沌安全通信系统。据此，通过硬件电路的实现，证明了最简单的类洛伦兹混沌电路和混沌保密通信电路的有效性和可行性。