A novel variant of NSN P systems, called numerical spiking neural P systems with a variable consumption strategy (NSNVC P systems), is proposed. Like the spiking rules consuming spikes in spiking neural P systems, NSNVC P systems introduce a variable consumption strategy by modifying the form of the production functions used in NSN P systems. Similar to the delay feature of the spiking rules, NSNVC P systems introduce a postponement feature into the production functions. The execution of the production functions in NSNVC P systems is controlled by two, i.e., polarization and threshold, conditions. Multiple synaptic channels are used to transmit the charges and the production values in NSNVC P systems. The proposed NSNVC P systems are a type of distributed parallel computing models with a directed graphical structure. The Turing universality of the proposed NSNVC P systems is proved as number generating/accepting devices. Detailed descriptions are provided for NSNVC P systems as number generating/accepting devices. In addition, a universal NSNVC P system with 66 neurons is constructed as a function computing device.

In biological neural networks, neurons transmit chemical signals through synapses, and there are multiple ion channels during transmission. Moreover, synapses are divided into inhibitory synapses and excitatory synapses. The firing mechanism of previous spiking neural P (SNP) systems and their variants is basically the same as excitatory synapses, but the function of inhibitory synapses is rarely reflected in these systems. In order to more fully simulate the characteristics of neurons communicating through synapses, this paper proposes a dynamic threshold neural P system with inhibitory rules and multiple channels (DTNP-MCIR systems). DTNP-MCIR systems represent a distributed parallel computing model. We prove that DTNP-MCIR systems are Turing universal as number generating/accepting devices. In addition, we design a small universal DTNP-MCIR system with 73 neurons as function computing devices.

The fuzzy reasoning numerical spiking neural P systems (FRNSN P systems) are proposed by introducing the interval-valued triangular fuzzy numbers into the numerical spiking neural P systems (NSN P systems). The NSN P systems were applied to the SAT problem and the FRNSN P systems were applied to induction motor fault diagnosis. The FRNSN P system can easily model fuzzy production rules for motor faults and perform fuzzy reasoning. To perform the inference process, a FRNSN P reasoning algorithm was designed. During inference, the interval-valued triangular fuzzy numbers were used to characterize the incomplete and uncertain motor fault information. The relative preference relationship was used to estimate the severity of various faults, so as to warn and repair the motors in time when minor faults occur. The results of the case studies showed that the FRNSN P reasoning algorithm can successfully diagnose single and multiple induction motor faults and has certain advantages over other existing methods.

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