Optimal control of a waste water cleaning plant.
Optimal impulsive harvest policy for time-dependent logistic equation with periodic coefficients.
Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources in population dynamics. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. They can be related to the emergence of biological species due to the intra-specific competition and random mutations. Various types of travelling waves are observed.
Pattern Formation of Competing Microorganisms in Sediments
We present a three species model describing the degradation of substrate by two competing populations of microorganisms in a marine sediment. Considering diffusion to be the main transport process, we obtain a reaction diffusion system (RDS) which we study in terms of spontaneous pattern formation. We find that the conditions for patterns to evolve are likely to be fulfilled in the sediment. Additionally, we present simulations that are consistent with experimental data from the literature. We...
Patterns of Zooplankton Functional Response in Communities with Vertical Heterogeneity: a Model Study
Parameterization of zooplankton functional response is crucial for constructing plankton models. Theoretical studies predict enhancing of system stability in case the response is of sigmoid type. Experiments on feeding in laboratories tell us in favor of non-sigmoid types for most herbivorous zooplankton species. However, recent field observations show that the overall functional response of zooplankton in the whole euphotic zone can exhibit a sigmoid behavior even when the response for the same...
Periodic solutions arising in ecology of mangroves
Periodic solutions for a stage-structure ecological model on time scales.
Periodic solutions of multispecies-competition predator-prey system with Holling's type III functional response and prey supplement.
Permanence and positive periodic solutions of a discrete delay competitive system.
Permanence in logistic and Lotka-Volterra systems with dispersal and time delays.
Permanence of predator-prey system with infinite delay.
Persistence and extinction of single population in a polluted environment.
Persistence in ratio-dependent models of consumer-resource dynamics.
Phytoplankton Dynamics: from the Behavior of Cells to a Transport Equation
We present models of the dynamics of phytoplankton aggregates. We start with an individual-based model in which aggregates can grow, divide, joint and move randomly. Passing to infinity with the number of individuals, we obtain a model which describes the space-size distribution of aggregates. The density distribution function satisfies a non-linear transport equation, which contains terms responsible for the growth of phytoplankton aggregates, their fragmentation, coagulation, and diffusion.
Plant-animal mutualistic networks: the architecture of biodiversity.
Population dynamics control in regard to minimizing the time necessary for the regeneration of a biomass taken away from the population
Population dynamics of Bithynia tentaculata
Population Dynamics of Grayling: Modelling Temperature and Discharge Effects
We propose a matrix population modelling approach in order to describe the dynamics of a grayling (Thymallus thymallus, L. 1758) population living in the Ain river (France). We built a Leslie like model, which integrates the climate changes in terms of temperature and discharge. First, we show how temperature and discharge can be related to life history traits like survival and reproduction. Second, we show how to use the population model to precisely examine the life cycle of grayling : estimated...
Population Growth and Persistence in a Heterogeneous Environment: the Role of Diffusion and Advection
The spatio-temporal dynamics of a population present one of the most fascinating aspects and challenges for ecological modelling. In this article we review some simple mathematical models, based on one dimensional reaction-diffusion-advection equations, for the growth of a population on a heterogeneous habitat. Considering a number of models of increasing complexity we investigate the often contrary roles of advection and diffusion for the persistence of the population. When it is possible we demonstrate...
Population growth and the environment: Can we eat the cake and have it?