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In this paper we investigate the following fractional order in time integrodifferential problem D t α u (t) + A u (t) = f (t , u (t)) + ∫ − ∞ t k (t − s) g (s , u (s)) d s , t ∈ R. Here, D t α is the Caputo derivative. We obtain results on the existence and uniqueness of (ω , c) -periodic mild solutions assuming that −A generates an analytic semigroup on a Banach space X and f, g, and k satisfy suitable conditions. Finally, an interesting example that fits our framework is given. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and uniqueness of (ω , Q) -periodic mild solutions for the following problem x ′ (t) = A x (t) + f (t , x (t)) , t ∈ R , on a Banach space X. Here, A is a closed linear operator which generates an exponentially stable C 0 -semigroup and the nonlinearity f satisfies suitable properties. The approaches are based on the well-known Banach contraction principle. In addition, a sufficient criterion is established for the existence and uniqueness of (ω , Q) -periodic mild solutions to the Hopfield-type neural network model. [ABSTRACT FROM AUTHOR]

In order to explore the behavioral mechanisms underlying aggregation of foragers on local resource patches, it is necessary to manipulate the location, quality and quantity of food patches. This requires careful control over the conditions in the foraging arena, which may be a challenging task in the case of aquatic resource-consumer systems, like that of freshwater zooplankton feeding on suspended algal cells. We present an experimental tool designed to aid behavioral ecologists in exploring the consequences of resource characteristics for zooplankton aggregation behavior and movement decisions under conditions where the boundaries and characteristics (quantity and quality) of food patches can be standardized. The aggregation behavior of Daphnia magna and D. galeata x hyalina was tested in relation to i) the presence or absence of food or ii) food quality, where algae of high or low nutrient (phosphorus) content were offered in distinct patches. Individuals of both Daphnia species chose tubes containing food patches and D. galeata x hyalina also showed a preference towards food patches of high nutrient content. We discuss how the described equipment complements other behavioral approaches providing a useful tool to understand animal foraging decisions in environments with heterogeneous resource distributions. [ABSTRACT FROM AUTHOR]