## 1 Introduction  
In the past recent decades, a variety of mathematical computational approaches have been implemented in different research fields such as fluid mechanic engineering [1; 2; 3; 4; 5; 6; 7; 8; 9], chemical engineering [10; 11; 12; 13; 14; 15; 16; 17; 18], electrical engineering [19; 20; 21; 22; 23; 24; 25; 26; 27; 28], telecommunication engineering [29; 30; 31; 32; 33; 34], computer engineering [35; 36; 37; 38; 39], petroleum engineering [40; 41; 42; 43; 44; 45; 46; 47], energy engineering [48; 49; 50], mathematics [51; 52; 53; 54; 55; 56; 57; 58; 59], environmental engineering [60; 61; 62], health and medical sciences [63; 64; 65], industrial engineering [66], etc. Among the various applied computational methods, artificial neural networks have been widely used, which demonstrates their capability. So, every effort in this field is of high importance. Spiking Neural Networks (SNNs) are a very attractive research area based on neuronal brain cells. The time-domain field in the SNN is the main concept that is based on the different models of neural networks. In SNNs, neurons can transmit data and information via synaptic connection, and this causes different levels of learning and memory in the human brain. In coupled neurons, when the presynaptic neuron is triggered by an applied stimulus current, this can release the voltage signals, this voltage can trigger the synaptic gap, and then the additional current is injected to the postsynaptic neurons, which is illustrated as a train of spiking behaviors in the post neurons. This behavior of neurons can be described by the spiking neuron models [67; 68; 69; 70; 71; 72]. The basic elements in this system are neurons, synapses, and glia [69; 73; 74; 75]. Neuron blocks are the important organs in CNS, which have several vital roles such as receiving, processing, and transmitting information to different parts of the human brain. On the other hand, synapses connect the neurons and are responsible for transferring data between neurons. Moreover, another cell called a glia can protect neurons in the CNS. Indeed, glia regulate the synaptic coupling between neurons. Thus, in the first step, the neurons' behaviors must be investigated in case of simulation and realization to obtain a compact and practical hardware. Neurons have different behaviors and reactions. These behaviors can follow the basic pattern, which can be modeled by the mathematical equations in [76; 77; 78; 79; 80; 81; 82; 83]. Two basic modeling systems have been presented. The first state is the biological model with biological parameters and reactions. Some basic models such as the Hodgkin-Huxley (HH) neuron model and the ADEX neuron model. These models have the biological aspects and may be a complex mathematical equation. On the other hand, SNN models are based on the spike timing patterns and less biological states. In this approach, some models such as the Izhikevic, FHN, and other models have been presented. Among these two modeling aspects, the SNN modeling may be better than the biological ones because of their low-cost implementations in hardware form. Indeed, when a compact neuron model (in hardware state) is required, the SNN models are better choices. As a result, a model named the Digital Spiking Silicon Neuron (DSSN) model is proposed [84]. This model was designed to simulate several classes of neurons by simple digital arithmetic circuits. The implementation of different models have been realized in different positions. Two basic selections of the implementation are analog and digital states [67; 68; 70; 71; 85; 86; 87; 88; 89; 90]. In analog implementation, CMOS elements are applied to achieve an analog architecture to follow the mathematical modeling of the neuron. This solution is fast, but it may suffer from long development timing. On the other hand, in the digital realization of neuronal models, a high amount of silicon may be required as well as high power consumption, but this solution can be very efficient in comparison to other methods.