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We consider stage-structured population models of intra- and inter-specific competition at immature life stages. A prototype delay model is derived for a single species that experiences larval competition. Its solutions are bounded for any birth function. Other ways of modelling the birth rate can lead to nonlinear integral equations. In some situations the technique of reducing an age-structured model to a system of delay equations applies. In the case of immature competition the delay equations cannot always be written down explicitly because their right hand sides depend on the solutions of the nonlinear ordinary differential equations that arise when one solves the nonlinear age-structured equations that determine the maturation rates in terms of the birth rates. This situation arises in the case of competition between two strains or species. However, in our two-strain competition model, vital properties of those right hand sides can be indirectly inferred using monotone systems theory. [ABSTRACT FROM AUTHOR]

Abstract: An equation , , is considered, where and are linear operators in a Hilbert space , , is a non-linear operator, and is a constant. Under some assumptions on and sufficient conditions are given for the solution to exist globally, i.e., for all , to be globally bounded, and to tend to zero at a specified rate as . [Copyright &y& Elsevier]

Abstract: This paper is concerned with the nonlinear stability of traveling wave fronts for nonlocal delayed reaction–diffusion equation. We prove that these traveling wave fronts are exponentially stable to perturbation in some exponentially weighted spaces, when the initial perturbation around the traveling wave fronts decays exponentially as , but the initial perturbation can be arbitrary large in other locations. The time decay rate is also obtained by weighted energy estimates. [Copyright &y& Elsevier]

For a delay differential system where the nonlinearity is motivated by applications of neural networks to spatiotemporal pattern association and can be regarded as a perturbation of a step function, we obtain the existence, stability and limiting profile of a phase-locked periodic solution using an approach very much similar to the asymptotic expansion of inner and outer layers in the analytic method of singular perturbation theory. [Copyright &y& Elsevier]