Bifurcation analysis and structural stability of simplicial oscillator populations
Can Xu, Xuebin Wang, Per Sebastian Skardal
Abstract
This paper studies the dynamics of coupled oscillator populations with higher-order interactions. These give rise to a continuum of abrupt desynchronization transitions and extensive multistability, allowing for memory and information storage. The authors propose an bifurcation analysis and a full description of the structural stability for the synchronized cluster states.
Topics & Concepts
Structural stabilityBifurcationStability (learning theory)MathematicsCluster (spacecraft)Saddle-node bifurcationBifurcation theoryDynamics (music)Statistical physicsBiological applications of bifurcation theoryDynamical systems theoryPhysicsHarmonic oscillatorMathematical analysisTopology (electrical circuits)Structural systemBifurcation diagramPure mathematicsTranscritical bifurcationApplied mathematicsControl theory (sociology)Nonlinear Dynamics and Pattern FormationNeural dynamics and brain functionstochastic dynamics and bifurcation