We investigate the stability and invariant manifolds of generalized Beddington model with the host population subject to the Allee effect.We obtain the condition for the existence of the fixed points and investigate the stability of the system.
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In this paper we develop the notion of contact orders for pairs of continuous self-maps (f, g) from ℝn, showing that the set Con(f, g) of all possible contact orders between f and g is a topological invariant (we remark that Con(f, id) = Per(f)). As an interesting application of this concept, we give sufficient conditions for the graphs of two continuous self-maps from ℝ intersect each other. We also determine the ordering of the sets Con(f, 0) and Con(f, h), for h ∈ Hom(ℝ) such that f ∘ h = h ∘ f. For this latter set we obtain a generalization of Sharkovsky’s theorem.
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