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Motivated by coupling an energy balance climate model and a two-species competition model for the bio-sphere, one is led to the study of functional reaction-diffusion equations with memory and a nonlocal Volterra operator. The existence of a trajectory attractor is established. The work is motivated by similar studies in (12) for a energy balance model with latent heat flux and uses techniques developed in (11) and (12). It is a continuation of (18), where an abstract global existence and boundedness result was established.

Trajectory attractors of energy balance climate models with bio-feedback