Stochastic Steering of Critical Transitions: Noise-Driven Power-Law Dynamics in First-Order Phase Transitions of Oscillatory Systems

The hysteretic nature of first-order phase transitions in coupled oscillators has attracted significant research interest due to their attributes of discontinuity and irreversibility. However, the inherent stochasticity and a variety of correlational constraints in the coupled oscillators often impede the understanding of the phase transition mechanisms. Here, we consider an ensemble of globally coupled Stuart–Landau oscillators in a fluctuation environment to decipher the mechanism of noise-driven stochastic steering of critical transitions by using modulation of the power-law function between dynamical parameters that can reshape phase-switching dynamics. Notably, we can facilitate a transition between continuous and discontinuous phases by adjusting the exponent in the power-law function, transcending heterogeneity or correlated coupling terms. When the natural frequency of uniformly coupled oscillators exhibits a power-law relationship with their natural amplitudes, and the scaling exponent of the power law falls within a specific range, the system reliably undergoes a first-order phase transition. Interestingly, while an increase in noise intensity does not alter this phenomenon, it does enhance the likelihood of synchronization events. Moreover, the critical parameter value for the transition in two distinct directions is observed to slide to the left with the strengthening of noise intensity, condensing the length of hysteresis loops. Furthermore, the decedent rate of the critical coupling strength during forward-phase transitions is significantly greater than the reverse process, implying that it is more sensitive to noise for forward switching. With the appearance of noise, the system starts to diverge and form distinct clusters that synchronize at various frequencies. Theoretical analysis and numerical simulations, harmoniously aligned, demonstrate that first-order phase transitions are susceptible to manipulation by power-law relationships between intrinsic parameters in the system in the fluctuating environment. Additionally, the necessary conditions for phase switching are attainable through the noise-induced stochastic bifurcation process in network evolution.