Optimal desynchronization of a noisy simplicial phase oscillator population based on backward stochastic differential equations (BSDEs)

This paper studies optimal desynchronization in a noisy population of phase oscillators with pairwise and triadic interactions. The model combines stochastic phase dynamics, higher-order collective coupling, and a finite-horizon control objective that penalizes both coherence and control effort. To capture different forms of collective organization, the formulation incorporates first-harmonic and second-harmonic coherence measures within the cost functional. The stochastic maximum principle is used to derive an adjoint backward stochastic differential equation coupled with the forward oscillator dynamics, leading to a forward-backward stochastic system that characterizes the optimal control. The resulting framework provides a systematic way to construct desynchronizing strategies in higher-order oscillator populations subject to random perturbations. The analysis clarifies how nonlinear collective interactions affect both the state evolution and the sensitivity structure of the optimality system, and it offers a general foundation for controlled coherence suppression in stochastic higher-order synchronization models.