Fuzzy differential inclusion in neural modeling

Abstract

Dynamical systems theory has helped brain scientists to cope better with brain complexity. In this paper, we proposed a novel approach to include uncertainty in dynamical system describing brain function such as one neuron or coupled neurons. Fuzzy dynamical systems represented by a set of fuzzy differential inclusions (FDI) are very convenient tools for modeling and simulation of various uncertain systems. We used fuzzy differential inclusion in modeling neural responses in several types of neurons. We showed that our results are very similar to real experimental data showing variability in neural responses. Further, we have shown that FDI has advantage in comparison with modeling uncertainty in neural systems with Stochastic Differential Equations (SDEs).