Chaotic cluster itinerancy and hierarchical cluster trees in electrochemical experiments

Area of Science:

• Complex Systems
• Nonlinear Dynamics
• Electrochemistry

Background:

• Globally coupled chaotic oscillators are fundamental in understanding complex system dynamics.
• Heterogeneity and noise are common factors influencing the behavior of coupled oscillator arrays.
• Dynamical clustering is a phenomenon observed in various complex systems.

Purpose of the Study:

• To investigate dynamical clustering in a heterogeneous array of 64 globally coupled chaotic electrochemical oscillators.
• To analyze the influence of coupling parameters and system heterogeneity on cluster formation and transitions.
• To characterize the nature of transitions between different cluster states.

Main Methods:

• Experimental setup with 64 globally coupled chaotic electrochemical oscillators.
• Introduction of controlled heterogeneity and noise in the oscillator array.
• Analysis of cluster configurations using hierarchical cluster trees.
• Observation and characterization of system dynamics and transitions over varying coupling parameters.

Main Results:

• Dynamical clustering was observed over specific ranges of the coupling parameter.
• Spontaneous changes in the number and configuration of clusters were detected.
• Transitions between cluster states included simple element switches, subcluster exchanges, and on-off intermittency at weaker coupling.

Conclusions:

• The heterogeneous array exhibits complex dynamical clustering behavior.
• System transitions are diverse, ranging from simple element rearrangements to complex subcluster exchanges.
• The observed on-off intermittency highlights the intricate dynamics at weaker coupling regimes.