Holling's ''hungry mantid'' model for the invertebrate functional response considered as a Markov process. III. Stable satiation distribution (Q1080799)

[Part I, II appeared in ibid. 22, 238-257 (1985) and for Part 0 see Zbl 0538.92021).] In this paper, we study an analytical model describing predatory behaviour. It is assumed that the parameter describing the predator's behaviour is its satiation. Using semigroup methods and compactness arguments we prove that a stable satiation distribution is reached if \(t\to \infty\). Furthermore, using a Trotter-Kato theorem we justify the transition to the much simpler problem that is obtained if the prey biomass tends to zero.