Modified Freeman model: a stability analysis and application to pattern recognition

The biologically realistic Freeman model of the olfactory cortex has been used to solve some engineering problems. However, due to the nature of the nonlinear function in the model, only numerical computer simulations can help explore the behavior of the system for different sets of control parameters. We modify the nonlinear function with a piecewise linear model and show that this simplified model exhibits the same qualitative behavior as the original one. Moreover, for this modified model, we employ the analytical tools of nonlinear dynamics to understand the system response for different parameter values. Finally, similar to the original system, we show that the modified system can be used as an auto-associative memory.