一种圆映射电路及其符号动力学研究

Study of a circle map circuit and its symbolic dynamics

设计了一种基于累积-释放模型的圆映射电路,从理论上对该电路的圆映射迭代关系和符号动力学特性进行了分析。通过调整电路和阈值信号参数,能使其工作状态发生变化,可处于各种周期态、混沌态等。研究了利用简单的逻辑判断直接获取符号序列的方法,并用微处理器和简单的逻辑电路构建了符号序列采集系统。从获得符号序列可以比较方便地计算周期、转数等,区别是周期、准周期还是混沌运动,为进一步的研究和应用提供一种有效途径。

Based on Integrate-and-Fire Model （ab. IFM）, a type of circle map circuit is proposed. The iterative relation and symbolic dynamics are analyzed theoretically. By adjusting parameters of the circuit and the threshold signal, the circuit may work in periodic and chaotic states. A method of acquiring symbolic sequence only by logic judgment is studied, and the system is also constructed by MCU and logic units. From the symbolic sequences, it is convenient to compute period and rotation, to distinguish periodic, quasiperiodic and chaotic motion. So an effective way is provided for further study and application.