How Can Anomalous-Diffusion Neural Networks Under Connectomics Generate Optimized Spatiotemporal Dynamics.

Area of Science:

• Neuroscience
• Complex Systems
• Mathematical Biology

Background:

• Spatiotemporal brain dynamics are linked to cognitive diseases like Alzheimer's.
• Connectomics and anomalous diffusion in neural networks are understudied in disease mechanisms.
• Optimizing brain dynamics offers therapeutic potential for neurological disorders.

Purpose of the Study:

• To model anomalous diffusion in a single-neuron network using connectomics.
• To apply nonlinear state feedback control for optimizing network dynamics.
• To investigate conditions influencing Turing instability and Hopf bifurcation.

Main Methods:

• Developed an anomalous-diffusion single-neuron model incorporating connectomics.
• Implemented a nonlinear state feedback control strategy.
• Analyzed characteristic equations to determine conditions for instabilities.
• Conducted numerical simulations to validate findings.

Main Results:

• The control strategy effectively optimizes network spatiotemporal dynamics.
• Identified key factors (delay, diffusion, fractional order) influencing dynamics.
• Determined conditions that inhibit Turing instability and delay Hopf bifurcation.
• Revealed the impact of self- and cross-diffusion on Turing instability.

Conclusions:

• Anomalous diffusion and connectomics provide a framework for understanding brain dynamics.
• Nonlinear control is a viable strategy for managing neural network instabilities.
• This approach offers a paradigm for nonequilibrium self-organization in biological systems.
• Findings have implications for developing treatments for neurodegenerative diseases.