Asynchronous Numerical Spiking Neural Membrane Systems with Local Synchronization

Since the spiking neural P system (SN P system) was proposed in 2006, it has become a research hotspot in the field of membrane computing. The SN P system performs computations through the encoding, processing, and transmission of spiking information and can be regarded as a third-generation neural network. As a variant of the SN P system, the global asynchronous numerical spiking neural P system (ANSN P system) is adaptable to a broader range of application scenarios. However, in biological neuroscience, some neurons work synchronously within a community to perform specific functions in the brain. Inspired by this, our work investigates a global asynchronous spiking neural P system (ANSN P system) that incorporates certain local synchronous neuron sets. Within these local synchronous sets, neurons must execute their production functions simultaneously, thereby reducing dependence on thresholds and enhancing control uncertainty in ANSN P systems. By analyzing the ADD, SUB, and FIN modules in the generating mode, as well as the INPUT and ADD modules in the accepting mode, this paper demonstrates the novel system's computational capacity as both a generator and an acceptor. Additionally, this paper compares each module to those in other SN P systems, considering the maximum number of neurons and rules per neuron. The results show that this new ANSN P system is at least as effective as the existing SN P systems.