Interspecific Competition of Plant Communities Based on Fractional Order Time Delay Lotka–Volterra Model

A novel time delay Lotka–Volterra (TDLV) model was developed by extending the concept of time delay from integer order to fractional order. The TDLV model was constructed to simulate the dynamics of aboveground biomass per individual of three dominant herbaceous plant species (Leymus chinensis, Agropyron cristatum, and Stipa grandis) in the typical grasslands of Inner Mongolia. Comparative analysis indicated that the TDLV model outperforms candidate models, such as Logistic, GM(1,1), GM(1,N), DGM(2,1), and Lotka–Volterra model, in terms of all fitting criteria. The results demonstrate that interspecies competition exhibits clear feedback and suppression effects, with Leymus chinensis playing a central role in regulating community dynamics. The system is locally stable and eventually converges to an equilibrium point, though Stipa grandis maintains relatively low biomass, requiring further monitoring. Time delays are prevalent in the system, influencing dynamic processes and causing damping oscillations as populations approach equilibrium.