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Real-time large-scale simulation of biological systems is a challenging task due to nonlinear functions describing biochemical reactions in the cells. Being fast, cost and power efficient alongside of capability to work in parallel have made hardware an attractive choice for simulation platform. This thesis proposes a neuromorphic platform for online Spike Timing Dependant Plasticity (STDP) learning, based on the COordinate Rotation DIgital Computer (CORDIC) algorithms. The implemented platform comprises two main components. First, the Izhikevich neuron model is modified for implementation using the CORDIC algorithm and simulated to ensure the model accuracy. Afterwards, the model was described as hardware and implemented on Field Programmable Gate Array (FPGA). Second, the STDP learning algorithm is adapted and optimized using the CORDIC method, synthesized for hardware, and implemented to perform on-FPGA online learning on a network of CORDIC Izhikevich neurons to demonstrate competitive Hebbian learning. The implementation results are compared with the original model and state-of-the-art to verify accuracy, effectiveness, and higher speed of the system. These comparisons confirm that the proposed neuromorphic system offers better performance and higher accuracy while being straightforward to implement and suitable to scale. New findings show that astrocytes are important parts of the information processing in brain and believed to be responsible for some brain diseases such as Alzheimer and Epilepsy. Astrocytes generate Ca$^{2+}$ waves and release neuro-transmitters over a large area. To study astrcoytes, one need to simulate large number of biologically realistic models of these cells alongside neuron models. Software simulation is flexible but slow. This thesis proposes a high-speed and low-cost digital hardware to replicate biological-plausible astrocyte and glutamate release mechanism. The nonlinear terms of these models were calculated using high-precision and cost-efficient algorithms. Subsequently, the modified models were simulated to study and validate their functions. Several hardware were developed by setting different constraints to investigate trade-offs and achieve best possible design. As proof of concept, the design was implemented on a FPGA device. Hardware implementation results confirmed the ability of the design to replicate biological cells in detail with high accuracy. As for performance, the proposed design turned out to be far more faster and area efficient than previously published works that targeted digital hardware for biological-plausible astrocytes. Spiking neurons, the models that mimic the biological cells in the brain, are described using ordinary differential equations. A common method to numerically solve these equations is Euler's method. An important factor that has a significant impact on the performance and cost of the hardware implementation or software simulation of spiking neural networks and yet its importance has been neglected in the published literature, is the time step in Euler's method. In this thesis, first the Izhikevich neuron's accuracy as a function of the time step was measured. It was uncovered that the threshold time step that Izhikevich neuron becomes unstable is an exponential function of the input current. Software simulation performance, including total computational time and memory usage were compared for different time steps. Afterwards, the model was synthesized and implemented on the FPGA. Hardware performance metrics such as speed, area and power consumption were measured for each time step. Results indicated that time step has a negative linear effect on the performance. It was concluded that by determining maximum input current to the neuron, larger time steps comparable to those used in the previous works could be employed.

Different architectures and techniques have developed in the neuromorphic field to mimic and investigate the activity of biological neural networks. This paper presents a set of piece-wise linear approximations of a two-dimensional Hindmarsh–Rose neuron model for digital circuit implementation to achieve higher speeds and lower hardware costs in large-scale implementation of the biological neural networks. The performance of the model was evaluated with a time domain signal error. Synthesis and hardware implementation on a field-programmable gate array, as a proof of concept, indicates that the proposed model reproduces several neuronal behaviors similar to the original model with higher performance and considerably lower implementation costs.