A Generalized Attention Deficit Disorder Chaotic Model With Soboleva Hyperbolic Tangent Functions

This work studies the problem of modeling Attention Deficit Disorder (ADD) using a previously reported one dimensional map, but by replacing its two hyperbolic tangent activation functions, with Soboleva hyperbolic tangent ones. This adds four new control parameters to the system, which significantly enhances its modeling freedom. Afterwards, the effect of these parameters on the model is studied, using tools of nonlinear analysis, like bifurcation, Lyapunov exponent, and phase diagrams. The emergence of chaos is prevalent, indicating the sensitivity of the model to external excitations. Numerous phenomena are also observed, like crisis, antimonotonicity, and shrimps. This new model can help delve deeper into the emergence of chaos in behavioral disorders.