Spiking neural membrane systems (SN P systems) are a class of bio-inspired models inspired by the activities and connectivity of neurons. Extensive studies have been made on SN P systems with synchronization-based communication, while further efforts are needed for the systems with rhythm-based communication. In this work, we design an asynchronous SN P system with resonant connections where all the enabled neurons in the same group connected by resonant connections should instantly produce spikes with the same rhythm. In the designed system, each of the three modules implements one type of the three operations associated with the edge detection of digital images, and they collaborate each other through the resonant connections. An algorithm called EDSNP for edge detection is proposed to simulate the working of the designed asynchronous SN P system. A quantitative analysis of EDSNP and the related methods for edge detection had been conducted to evaluate the performance of EDSNP. The performance of the EDSNP in processing the testing images is superior to the compared methods, based on the quantitative metrics of accuracy, error rate, mean square error, peak signal-to-noise ratio and true positive rate. The results indicate the potential of the temporal firing and the proper neuronal connections in the SN P system to achieve good performance in edge detection.

尖峰神经膜系统（SN P 系统）是一类受神经元活动和连接启发的仿生模型。人们对基于同步通信的 SN P 系统进行了广泛的研究，而对于基于节律通信的系统还需要进一步的努力。在这项工作中，我们设计了一个具有共振连接的异步 SN P 系统，其中通过共振连接连接的同一组中所有启用的神经元应立即产生具有相同节奏的尖峰。在设计的系统中，三个模块中的每一个都实现与数字图像边缘检测相关的三种操作中的一种，并且它们通过谐振连接相互协作。提出了一种称为 EDSNP 的边缘检测算法来模拟所设计的异步 SN P 系统的工作。对EDSNP和相关边缘检测方法进行了定量分析，以评估EDSNP的性能。基于准确率、错误率、均方误差、峰值信噪比和真阳性率的定量指标，EDSNP 在处理测试图像方面的性能优于对比方法。结果表明 SN P 系统中的时间放电和适当的神经元连接具有在边缘检测中实现良好性能的潜力。