In the literature, the parabolic function of the Izhikevich Neuron Model (IzNM) is transformed to the Piecewise Linear (PWL) functions in order to make digital hardware implementations easier. The coefficients in this PWL functions are identified by utilizing the error-prone classical step size method. In this paper, it is aimed to determine the coefficients of the PWL functions in the modified IzNM by using the stochastic optimization methods. In order to obtain more accurate results, Genetic Algorithm and Artificial Bee Colony Algorithm (GA and ABC) are used as alternative estimation methods, and amplitude and phase errors between the original and the modified IzNMs are specified with a newly introduced error minimization algorithm, which is based on the exponential forms of the complex numbers. In accordance with this purpose, GA and ABC algorithms are run 30 times for each of the 20 behaviors of a neuron. The statistical results of these runs are given in the tables in order to compare the performance of three parameter-search methods and especially to see the effectiveness of the newly introduced error minimization algorithm. Additionally, two basic dynamical neuronal behaviors of the original and the modified IzNMs are realized with a digital programmable device, namely FPGA, by using new coefficients identified by GA and ABC algorithms. Thus, the efficiency of the GA and ABC algorithm for determining the nonlinear function parameters of the modified IzNM are also verified experimentally.