INVERTEBRATES AND CATTLE POPULATION DYNAMICS IN A GRASSLAND ENVIRONMENT: A NONLINEAR INTER-SPECIFIC COMPETITION MODEL

Abstract

In the proposed study, a nonlinear model is developed to explore the interactive dynamics between cattle and invertebrates when they coexist in a grassland system and compete with one another for the same resource — the grass biomass. The constructed model is theoretically investigated using the qualitative theory of differential equations to show the system’s rich dynamical properties, which are crucial for maintaining the ecosystem’s balance in grasslands. The qualitative findings show that, depending on the parameter combinations, the system not only displays stability of many equilibrium states but also experiences transcritical and Hopf bifurcations. The model results support the idea that inter-specific competition between cattle and invertebrates does not always produce regular dynamic patterns but may also produce periodic and destabilizing patterns. The model’s outputs may assist in striking a balance between pasture and natural grass biomass in grassland with the invertebrates.