Final answer:
To assess whether the steady state is globally stable for probiotic and pathogen bacteria, one must observe if population levels off at a stable value regardless of initial size, indicating an equilibrium in the ecosystem.
Step-by-step explanation:
To determine whether the steady state for probiotic and pathogen bacteria is globally stable with the given values for a (growth rate) and K (carrying capacity), you would need to observe whether the population dynamics reach the same steady state from any initial population size. In such a steady state, the ecosystem will display properties where it remains in equilibrium despite disturbances, and the growth pattern of the bacterial population will reach a plateau known as the stationary phase, where the rate of cell division and cell death are roughly equal.
If the simulation results consistently show that the population growth of both probiotic and pathogenic bacteria levels off at a stable value regardless of the starting population size, then yes, the steady state is considered to be globally stable. This implies that the ecosystem exhibits stability and resilience, with the ability to maintain equilibrium conditions over time.