Chapter Twelve - Dynamics and implementation techniques of fractional-order neuron models: a survey

Abstract

The spiking neural networks (SNNs) form a special class of artificial neural networks (ANNs), which are brain-inspired connectionist systems. They are the main candidates for the proficient computing based on parallel processing. SNNs are an assembly of a large number of small processing units known as neuron models that communicate by sequences of spikes. Neurons are interconnected to each other in a well-defined pattern that allows communication between them. The biological neuron is represented by the neuron model which mathematically characterizes the biological neuron and depicts certain of its properties like generating an electric pulse across the cell membrane. The neuron models govern the dynamics of the neuron such as spiking, resting, periodic and excitable spiking, bursting, chaos, and bifurcation. The quantification of the neuron dynamics involves the measurement/portraying of the limit cycle, eigenvalues, the bifurcation diagram, the Lyapunov exponent, nullclines, etc. In addition, after studying the dynamics of neuron models, they are implemented for application purposes. The implementation includes both software implementation and hardware approaches (i.e., analog, digital, and mixed-mode implementations). In contemporary neuron modeling, fractional-order differential equations are proven to be a paramount candidate for understanding the mathematical dynamical behavior underlying the experimental data collected by the neurobiologists. In this chapter, the detailed background and mathematical aspects of FO dynamical systems will be discussed in connection with existing literature. In addition, various FO implementation techniques from analog to digital hardware will be reviewed.