Cluster Synchronization in Multilayer Networks: A Fully Analog Experiment with LC Oscillators with Physically...

Area of Science:

• Nonlinear dynamics
• Complex networks
• Experimental physics

Background:

• Multilayer networks exhibit complex dynamics.
• Cluster synchronization is a key phenomenon in coupled oscillators.
• Understanding coupling effects is crucial for network behavior.

Purpose of the Study:

• To experimentally investigate cluster synchronization in a two-layer network of Colpitts oscillators.
• To characterize different synchronized states arising from varying coupling strengths.
• To explore the impact of dissimilar coupling types within a multilayer network.

Main Methods:

• Experimental realization of a multilayer network using electronic Colpitts oscillators.
• Systematic variation of coupling parameters in the two interaction layers.
• Application of bifurcation analysis to identify state transitions.
• Computation of transverse Lyapunov exponents for stability analysis.

Main Results:

• Observation of multiple cluster synchronization states.
• Identification of four distinct synchronized states, ranging from full synchronization to clustered quasiperiodicity.
• Experimental demonstration of a clustered quasiperiodic state, a novel finding.
• Analysis of networks with fundamentally dissimilar coupling types across layers.

Conclusions:

• Multilayer networks can exhibit rich cluster synchronization patterns.
• The interplay of coupling in different layers dictates emergent synchronized states.
• This study provides the first experimental evidence of clustered quasiperiodic states in such systems.
• The findings advance the understanding of complex dynamics in coupled oscillator networks.