Dynamic Analysis of a Generalized Attention Deficit Disorder model with Soboleva Activation Functions

This work studies a modified chaotic neural network model consisting of two neurons, for modeling Attention Deficit Disorder (ADD). Considering an existing one-dimensional model from the literature, its two activation functions are replaced by the Soboleva hyperbolic tangent function. This change introduces four new control parameters to the system. The effect of these parameters to the system is extensively studied through a collection of phase, bifurcation, and Lyapunov exponent diagrams. Changing each of these parameters brings changes to the model’s behavior, so the modified model is a significant generalization of the original one. Many phenomena are observed, including period doubling route to chaos, period halving route to period-1, crisis, antimonotonicity, coexisting attractors, and shrimps. The newly introduced degrees of freedom could provide a new direction towards modeling behavioral disorders using different activation functions.