Dynamic analysis of a generalized attention deficit disorder model with Soboleva activation functions

Area of Science:

• Computational Neuroscience
• Dynamical Systems Theory
• Mathematical Psychology

Background:

• Existing one-dimensional chaotic neural network models offer limited flexibility for complex phenomena.
• Modeling behavioral disorders like attention deficit disorder (ADD) requires sophisticated computational frameworks.

Purpose of the Study:

• To investigate a modified two-neuron chaotic neural network model for attention deficit disorder (ADD).
• To explore the impact of newly introduced control parameters on the model's dynamics.

Main Methods:

• Replaced original activation functions with the Soboleva hyperbolic tangent function.
• Analyzed system behavior using phase diagrams, bifurcation diagrams, and Lyapunov exponent calculations.

Main Results:

• The modified model demonstrated a significant generalization of the original system.
• Observed complex dynamical phenomena including period doubling, chaos, crisis, antimonotonicity, coexisting attractors, and shrimps.
• Demonstrated the influence of four new control parameters on system dynamics.

Conclusions:

• The modified chaotic neural network provides a more flexible framework for modeling behavioral disorders.
• The introduction of new activation functions and parameters offers novel insights into the complex dynamics of neurological conditions.