Synchronization in an array of output-coupled Boolean networks with time delay
IEEE Transactions on Neural Networks and Learning Systems
|November 25, 2014
Summary
This study analyzes synchronization in coupled Boolean networks (BNs) with time delays. It provides conditions for achieving synchronization in these complex systems, illustrated with an epigenetic example.
Area of Science:
- Systems Biology
- Control Theory
- Computational Neuroscience
Background:
- Boolean networks (BNs) are widely used to model complex biological systems.
- Synchronization is a key phenomenon in coupled dynamical systems, relevant to biological processes.
- Time delays in network outputs and states can significantly impact system dynamics.
Purpose of the Study:
- To analytically study synchronization in arrays of coupled deterministic Boolean networks with time delays.
- To investigate two models: one with output delays and one without.
- To derive conditions for synchronization in delay-coupled BNs.
Main Methods:
- Utilizing algebraic representations of logical dynamics.
- Applying the semitensor product of matrices technique.
- Analyzing systems with equal state and output delays.
Main Results:
- Derivation of necessary and sufficient conditions for synchronization in delay-coupled BNs.
- Demonstration of synchronization phenomena in the considered models.
- Validation through illustrative examples, including a practical epigenetic model.
Conclusions:
- The study provides a rigorous framework for understanding synchronization in delayed Boolean networks.
- The derived conditions offer practical insights for controlling and designing synchronized biological systems.
- The findings have implications for modeling and analyzing complex biological networks with time delays.
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