In recent decades, marine ecologists have conducted extensive field work and experiments to understand the interactions between bacteria and bacteriophage (phage) in marine environments. This dissertation provides a detailed rigorous framework for gaining deeper insight into these interactions. Specific features of the dissertation include the design of a new deterministic Lotka-Volterra model ...

A food web in a chemostat is considered in which an arbitrary number of competitor populations compete for a single, essential, nonreproducing, growth-limiting substrate, and an arbitrary number of predator populations prey on some or all of the competitor populations. Although any number of predator populations may prey on the same competitor population, each predator population preys on only ...

Whether a new technology can successfully compete against an established one, and either hold its own or indeed replace the older technology depends on many factors, not least of which is the ability of the innovators to anticipate how the market and the existing firms will react to the newcomer. In this paper, we describe and contrast the behaviours of a quadratic recurrence relation derived f...

FROM purely theoretical considerations Lotka (1920) and Volterra (1926) concluded that a biological system consisting of two interdependent species (predator and prey) will exhibit regular periodic fluctuations in respect to the absolute and relative abundance of each species, even when random fluctuations due to external environmental factors have been eliminated. So far as is known this concl...

Synopsis Most of the convergence results appearing so far for delayed Lotka-Volterra-type systems require that undelayed negative feedback dominate both delayed feedback and interspecific interactions. Such a requirement is rarely met in real systems. In this paper we present convergence criteria for systems without instantaneous feedback. Roughly, our results suggest that in a Lotka-Volterra-t...

A general framework for age-structured predator-prey systems is introduced. Individuals are distinguished into two classes, juveniles and adults, and several possible interactions are considered. The initial system of partial differential equations is reduced to a system of (neutral) delay differential equations with one or two delays. Thanks to this approach, physically correct models for pred...

In the case of a critical point being a center, the isochronicity problem (or linearizability problem) is far to be solved in general. A progressive way to find necessary conditions for isochronicity is to compute period constants. In this paper, we establish a new recursive algorithm of calculation of the so-called generalized period constants. Furthermore, we verify the new algorithm by the e...

This paper is concerned with the existence of traveling wave solutions in delayed reaction diffusion systems which at least contain multi-species competition, cooperation and predator-prey models with diffusion and delays. By introducing the mixed quasimonotone condition and the exponentially mixed quasimonotone condition, we reduce the existence of traveling wave solutions to the existence of ...

Negative cross-diiusion has been identiied as a factor increasing the possibility of spatio-temporal instabilities in Lotka-Volterra equations. But such terms have been considered as quite rare in ecological modeling, since imply deceitful prey-predator relationships. We show that negative cross-diiusion appears naturally in reaction diiusion equations obtained using a simple mean eld decouplin...

A novel coordinate transformation is used to reduce a simple generalization of the Lotka-Volterra dynamical system to a single second-order autonomous ordinary differential equation. Formal analytic solutions to this differential equation are presented which are shown to reduce to the recently obtained solution to the LotkaVolterra system [C. M. Evans and G. L. Findley, J. Math. Chem. 25 (1999)...