Speaker
Description
In this work, we revisit classical three-dimensional Lotka-Volterra two
prey-one-predator models with direct prey competition. Employing a rescaling technique, we reduce the system to a simpler model with eight key parameters.With minimal assumptions, all parameters are grouped into four generic categories with a total of nine subcases, which are further refined into 56 sub-items to explore diverse dynamical behaviors, including the globally asymptotically stabilities and bistabilities of boundary equilibria, the existence and stability of the positive equilibrium, the existence of periodic solutions, and the complex dynamics of some solutions. Many results are novel, most findings are shown analytically, and verified numerically.
Fromabiological perspective, we find three competition interactions among species: the resource, apparent, and trade-off competitions. These explore how the interplay between direct competition for resources, apparent competition mediated by a shared predator, and trade-off competition dictates species survival and ecosystem diversity. By symmetry and without loss of generality, we assume that one prey species (e.g., u1) is superior in its birth-to-consumption ratio, the apparent competition. Biological implications are provided to interpret the origin of the dynamics
