Some boundedness results for systems of two rational difference equations

Original · EN

We study kth order systems of two rational difference equations xₙ=α+∑ᵏᵢ₌₁βᵢxₙ₋ᵢ + ∑ᵏᵢ₌₁γᵢyₙ₋ᵢA+∑ᵏⱼ₌₁Bⱼxₙ₋ⱼ + ∑ᵏⱼ₌₁Cⱼyₙ₋ⱼ, n, yₙ=p+∑ᵏᵢ₌₁δᵢxₙ₋ᵢ + ∑ᵏᵢ₌₁εᵢyₙ₋ᵢq+∑ᵏⱼ₌₁Dⱼxₙ₋ⱼ + ∑ᵏⱼ₌₁Eⱼyₙ₋ⱼ, n. In particular we assume non-negative parameters and non-negative initial conditions. We develop several approaches which allow us to extend well known boundedness results on the kth order rational difference equation to the setting of systems in certain cases.