Minimal Pinning Control for Oscillatority of Boolean Networks

Area of Science:

• Control theory
• Computational biology
• Network science

Background:

• Boolean networks (BNs) are widely used to model complex biological systems.
• Controlling instability (oscillatority) in BNs is crucial for understanding system dynamics.
• Existing control methods can be computationally intensive.

Purpose of the Study:

• To develop minimal pinning control strategies for Boolean networks.
• To address oscillatority (instability) in BNs using algebraic state space representations.
• To reduce control costs and computational complexity.

Main Methods:

• Derived two criteria for BN oscillatority from state transition matrix (STM) and network structure (NS).
• Proposed distributed pinning control (DPC) methods: STM-based DPC and NS-based DPC.
• Introduced hybrid pinning control (HPC) combining DPC and conventional pinning control (CPC).

Main Results:

• STM-based DPC allows control of arbitrary nodes based on equation solvability.
• NS-based DPC identifies pinning control nodes (PCNs) using network structure, reducing complexity.
• Both DPC methods are simple, concise, and depend only on local in-neighbors.

Conclusions:

• The proposed STM-based and NS-based DPC offer efficient and simplified control for BNs.
• These methods provide a new direction for reducing control costs and computational demands.
• Simulations on gene networks demonstrate the effectiveness of the theoretical results.