Dynamical regulation of nonlinear term and frequency heterogeneity in fractional-order Stuart–Landau oscillators

This paper investigates how dynamical behaviors are regulated by nonlinearity and frequency heterogeneity in networks of fractional-order Stuart–Landau oscillators with a nonisochronous parameter. Our main finding is the antagonistic interplay between these two factors. First, increasing the nonlinearity coefficient suppresses the oscillation in synchronization levels mediated by chimera states and reduces the variety of chimera states, eventually eliminating them. That is, stronger nonlinearity promotes synchronization and suppresses chimera states, a conclusion further supported by synchronous stability analysis. Second, while the system can sustain synchronized oscillations under weak frequency heterogeneity, strong heterogeneity destroys them. Thus, increased frequency heterogeneity tends to suppress synchronization and, conversely, promote chimera states. Finally, we explore this antagonism and find that frequency heterogeneity acts as the dominant factor governing the system’s dynamical state. In contrast, the nonlinearity coefficient only exerts a limited buffering effect and cannot reverse the overall trend of synchronization degradation induced by increasing frequency heterogeneity. This work not only deepens the understanding of nonlinear and heterogeneous effects in fractional-order oscillatory systems but also provides theoretical implications for the control of synchronization and chimera states in nonisochronous, memory-dependent dynamical networks.