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Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative
Takashi Nishikawa1, Adilson E Motter
1Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA. tnishika@clarkson.edu
Summary
Synchronization in complex networks relies on network structure. This study reveals that quantized interaction strength, not just connection complexity, optimizes synchronization, showing "less can be more" by using negative interactions or link removals.
Area of Science:
- Complex systems
- Network science
- Dynamical systems theory
Background:
- Synchronization is a fundamental phenomenon in decentralized dynamical systems.
- The role of interaction network topology in collective synchronization is not fully understood.
- Existing paradigms assume pairwise synchronization interactions directly translate to collective synchronization.
Purpose of the Study:
- To challenge the prevailing paradigm regarding network properties and collective synchronization.
- To characterize networks that exhibit optimal synchronization, minimal coupling cost, and maximal robustness.
- To explore methods for improving synchronization properties through network modifications.
Main Methods:
- Analysis of oscillator networks with varying complexity and interaction strengths.
- Investigation of the relationship between network topology, interaction strength, and synchronization metrics.
- Exploration of the effects of negative interactions and link removals on synchronization.
Main Results:
- Networks with optimal synchronization, minimal coupling cost, and maximal robustness possess quantized total interaction strength.
- Total interaction strength, rather than arbitrary complexity, constrains the number of connections for optimal synchronization.
- Negative interactions and link removals can systematically enhance synchronization properties in both directed and undirected networks.
Conclusions:
- The study challenges the assumption that pairwise synchronization interactions always promote collective synchronization.
- Quantized interaction strength is a key factor for achieving optimal synchronization, robustness, and efficiency.
- Network optimization for synchronization can be achieved by strategically introducing negative interactions or removing links, demonstrating a 'less is more' principle.
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