Chaotic dynamics analysis and digital hardware design of the Izhikevich neuron model

Neuromorphic hardware facilitates the fast and energy-efficient implementation of neural network-based artificial intelligence, making it particularly effective for addressing brain-inspired robotic challenges. The advancement of neuromorphic algorithms can continue to evolve in accordance with the principles of neural computing and the architectures of neural networks that draw inspiration from biological neural systems. In this perspective, we proposed a modified Izhikevich model that imitates the biological behaviors of the original neuron model using the Coordinate Rotation Digital Computer (CORDIC) algorithm. By employing adder and shifter operations to remove multipliers, the proposed method presents an effective digital hardware implementation of the Izhikevich model. The CORDIC-based Izhikevich model can accurately replicate the biological behaviors of the original model, according to error analysis and dynamic evaluations. Furthermore, the major goal of this work is to identify stable equilibrium points, chaotic regimes, and transitions between various dynamical states by investigating the dynamic behaviors of the proposed Izhikevich model under varying parameters. For this reason, the transitions from periodic to chaotic behavior are defined by applying numerical analyses, which include bifurcation diagrams and the maximum Lyapunov exponent. The potential for hardware implementation with high speed is the proposed model's superiority over the original model, while it has a high compatibility level. In order to verify the effectiveness of the suggested hardware in comparison to previous studies, four cost functions are introduced based on operation frequency, power, and errors. Applying this method to the Spartan6 board can increase the speed of the proposed model by approximately 3.18 times compared to the original model. Therefore, the suggested hardware, whose features include low error rates, acceptable power consumption, and frequency capabilities, exhibits efficiency and impact in a variety of applications, such as modeling learning processes in the nervous system that are based on nonlinear and chaotic behaviors.