Periodic coupling inhibits second-order consensus on networks
Fabian Baumann1, Igor M Sokolov1,2, Melvyn Tyloo3
1Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, 12489 Berlin, Germany.
Physical Review. E
|December 17, 2020
Summary
Time-periodic coupling modulations can unexpectedly prevent consensus in second-order systems. This study identifies specific frequencies that induce parametric resonance, hindering collective agreement in networks.
Area of Science:
- Network science
- Control theory
- Dynamical systems
Background:
- Consensus algorithms are crucial for distributed decision-making and multi-agent coordination.
- Second-order consensus models incorporate Newtonian dynamics of physical agents.
Purpose of the Study:
- To investigate the impact of time-periodic coupling modulations on second-order consensus models.
- To identify mechanisms that inhibit the formation of collective consensus states.
Main Methods:
- Spectral decomposition of the consensus model.
- Analytical derivation of conditions for parametric resonance.
- Extension of parametric resonance theory to networks with time-periodic couplings.
Main Results:
- Small time-periodic coupling modulations can inhibit consensus formation.
- Parametric resonance is induced at specific intermediate coupling frequencies.
- Resonance frequencies are precisely predicted and linked to the network's Laplacian spectrum.
Conclusions:
- Time-periodic coupling modulations can disrupt consensus in second-order systems.
- The study provides a precise formalism to predict and quantify resonance phenomena in such networks.
- Findings are crucial for designing robust coordination strategies in networked systems.
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