Fractional-order Spiking Systems
Fractional Calculus is a field in mathematics that studies the non-integer order derivatives and integrals where the order can be rational, real, or even complex. It presents a more accurate explanation of physical behaviors due to its ability to capture nonlocal dynamics involving long-term memory effects. Such advantage is very useful to fields like neuroscience where the memory is xx
In this project, we explore first the fractional-order models that mimic better the in vivo/ in vitro neuron behaviors. Such models are achieved at the expense of higher computations. Hence, we explore different numerical techniques and evaluate the computational complexity.
Secondly, we study the behavior of spiking neural networks involving fractional-order synaptic and neuron models. We explore emerging training methods such as the three-factor rule performing supervised and unsupervised learning. In addition, we study fractional-order gradient techniques to better train neural networks and to achieve faster convergence.
Third, we explore possible applications of fractional-order models in neuroscience and working memory problems.
Related Publications:
- A. M. AbdelAty, M. E. Fouda, and A. M. Eltawil, Parameter Estimation of Two Spiking Neuron Models with Meta-Heuristic Optimization Algorithms, Frontiers in Neuroinformatics, 2022 Codes.
Collaborators:
- Dr. Amr Abdelaty
Students: