Memory selection and information switching in oscillator networks with higher-order interactions

Abstract

We study the dynamics of coupled oscillator networks with higher-order interactions and their ability to store information. In particular, the fixed points of these oscillator systems consist of two clusters of oscillators that become entrained at opposite phases, mapping easily to information more commonly represented by sequences of 0's and 1's. While $2^N$ such fixed point states exist in a system of $N$ oscillators, we find that a relatively small fraction of these are stable, as chosen by the network topology. To understand the memory selection of such oscillator networks, we derive a stability criterion to identify precisely which states are stable, i.e., which pieces of information are supported by the network. We also investigate the process by which the system can switch between different stable states when a random perturbation is applied that may force the system into the basin of attraction of another stable state.

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Cited by in corpus (12)

• Higher-order simplicial synchronization of coupled topological signals
• Higher-order interactions improve optimal collective dynamics on networks
• Spectrum of extensive multiclusters in the Kuramoto model with higher-order interactions
• Consensus on simplicial complexes, or: The nonlinear simplicial Laplacian
• Multistability in coupled oscillator systems with higher-order interactions and community structure
• Enlarged Kuramoto Model: Secondary Instability and Transition to Collective Chaos
• Geometry, Topology and Simplicial Synchronization
• Collective dynamics on higher-order networks
• Global topological synchronization of weighted simplicial complexes
• Tiered synchronization in coupled oscillator populations with interaction delays and higher-order interactions
• Higher-order synchronization on the sphere
• Heteroclinic Switching between Chimeras in a Ring of Six Oscillator Populations