Use of Izhikevich neurons in Hopfield models

The Izhikevich chaotic neuron model represents a considerable advancement in computational neuroscience by offering a mathematical framework that closely mirrors the behavior of biological neurons, especially in generating chaotic or complex spiking patterns seen in the brain. This model has garnered attention due to its ability to replicate a wide range of real-life neural dynamics, including bursting and tonic spiking, which are fundamental to understanding the complexities of neural communication and processing. On the other hand, Hopfield networks, a type of recurrent neural network, have long been recognized for their ability to serve as content- addressable memory systems, storing and recalling information based on associative dynamics. Often described as spin glass systems, Hopfield networks operate by finding stable states or patterns within the neural network, emulating certain memory functions of the human brain. Recently, research into innovative activation functions has opened new possibilities for enhancing the capabilities of recurrent networks. The chaotic activation functions, in particular, present an intriguing area of exploration within Hopfield networks. This article investigates the effects of embedding these chaotic activation functions in Hopfield networks, examining how they influence the network's stability, adaptability, and efficiency. Through this exploration, we aim to reveal the impact of chaos on the network's dynamics, providing insights that could potentially lead to improved performance in applications requiring complex memory and associative processing. The study contributes to the growing field of neuromorphic engineering, with implications for both artificial intelligence and neuroscience.