How to Predict Bifurcations Induced by Fractional Order in Delayed Large-Scale Neural Networks

Area of Science:

• Complex Systems
• Dynamical Systems Theory
• Computational Neuroscience

Background:

• Large-scale neural networks exhibit complex dynamics.
• Fractional calculus offers novel ways to model system memory and hereditary properties.
• Bifurcations in dynamical systems signify critical changes in behavior.

Purpose of the Study:

• Introduce fractional delayed large-scale neural networks with complex topology.
• Investigate fractional order-induced bifurcations and stability.
• Develop a method for determining optimal fractional order for stability.

Main Methods:

• Mason's diagram and Coates' flow graph decomposition for network analysis.
• Global element concept for eigenroot distribution analysis.
• Implicit function array curve method for stability interval determination.

Main Results:

• Established correlation between artificial and graphical neural networks.
• Analyzed Hopf bifurcation onset with increasing synaptic transmission delays.
• Determined optimal fractional order-dependent stability intervals.
• Demonstrated that reduced fractional order improves steady-state performance but can lead to oscillations if below a critical threshold.

Conclusions:

• Increased delay triggers Hopf bifurcation in these networks.
• Fractional order significantly impacts system stability and performance.
• Proposed prediction algorithm aids in selecting optimal fractional order for large-scale complex networks.