Creative dynamics approach to neural intelligence

Area of Science:

• * Nonlinear Dynamics
• * Computational Neuroscience
• * Systems Biology

Background:

• * Artificial neural networks exhibit rigid behavior, limiting their biological modeling capabilities.
• * Existing dynamical systems struggle to replicate the flexibility of biological systems.
• * Novel approaches are needed to develop more adaptable computational models.

Purpose of the Study:

• * Introduce a new class of dynamical systems termed 'unpredictable systems'.
• * Develop a novel modeling paradigm for biological behavior using nonlinear dynamics.
• * Address the limitations of artificial neural networks in mimicking biological complexity.

Main Methods:

• * Exploited a novel paradigm in nonlinear dynamics based on terminal attractors and repellers.
• * Developed non-Lipschitzian dynamics by failing the Lipschitz condition.
• * Analyzed coupled activation and learning dynamical equations with zero Jacobian and failing Lipschitz conditions.

Main Results:

• * Demonstrated a multi-choice response to periodic external excitations in non-Lipschitzian dynamics.
• * Introduced and analyzed 'unpredictable systems' with pathological characteristics (zero Jacobian, failing Lipschitz conditions).
• * Showcased that unpredictable systems can be controlled by sign strings to reproduce prescribed behaviors.

Conclusions:

• * Unpredictable systems offer a new paradigm for modeling biological behavior with enhanced flexibility.
• * The multi-choice response and controllability of these systems open new avenues in computational neuroscience.
• * This approach provides a foundation for developing more sophisticated and adaptive artificial biological models.