Plants are often subjected to periods of soil and atmospheric water deficit during their life cycle. The frequency of such phenomena is likely to increase in the future even outside today's arid/semi-arid regions. Plant responses to water scarcity are complex, involving deleterious and/or adaptive changes, and under field conditions these responses can be synergistically or antagonistically modified by the superimposition of other stresses. This complexity is illustrated using examples of woody and herbaceous species mostly from Mediterranean-type ecosystems, with strategies ranging from drought-avoidance, as in winter/spring annuals or in deep-rooted perennials, to the stress resistance of sclerophylls. Differences among species that can be traced to different capacities for water acquisition, rather than to differences in metabolism at a given water status, are described. Changes in the root : shoot ratio or the temporary accumulation of reserves in the stem are accompanied by alterations in nitrogen and carbon metabolism, the fine regulation of which is still largely unknown. At the leaf level, the dissipation of excitation energy through processes other than photosynthetic C-metabolism is an important defence mechanism under conditions of water stress and is accompanied by down-regulation of photochemistry and, in the longer term, of carbon metabolism.

The paper addresses the computation of normal forms for some Partial Functional Differential Equations (PFDEs) near equilibria. The analysis is based on the theory previously developed for autonomous retarded Functional Differential Equations and on the existence of center (or other invariant) manifolds. As an illustration of this procedure, two examples of PFDEs where a Hopf singularity occurs on the center manifold are considered.

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We consider a predator᎐prey system with one or two delays and a unique positive equilibrium E#. Its dynamics are studied in terms of the local stability of E# and of the description of the Hopf bifurcation that is proven to exist as one of Ž . the delays taken as a parameter crosses some critical values. We also consider a reaction᎐diffusion system with Neumann conditions, resulting from adding one spatial variable and diffusion terms in the previous model. The spectral and bifurcation analysis in the neighborhood of E#, now as a stationary point of this latter system, is addressed and the results obtained for the case without diffusion are applied. ᮊ

We develop a new approach to obtain the existence of travelling wave solutions for reaction–diffusion equations with delayed non-local response. The approach is based on an abstract formulation of the wave profile as a solution of an operational equation in a certain Banach space, coupled with an index formula of the associated Fredholm operator and some careful estimation of the nonlinear perturbation. The general result relates the existence of travelling wave solutions to the existence of heteroclinic connecting orbits of a corresponding functional differential equation, and this result is illustrated by an application to a model describing the population growth when the species has two age classes and the diffusion of the individual during the maturation process leads to an interesting non-local and delayed response for the matured population.