Positive periodic solutions of a discrete mutualism model with time delays.
Possibly Longest Food Chain: Analysis of a Mathematical Model
We consider the number of trophic levels in a food chain given by the equilibrium state for a simple mathematical model with ordinary differential equations which govern the temporal variation of the energy reserve in each trophic level. When a new trophic level invades over the top of the chain, the chain could lengthen by one trophic level. We can derive the condition that such lengthening could occur, and prove that the possibly longest chain is globally stable. In some specific cases,...
Protector control: Extension to a class of nonlinear distributed systems
We present an extension of the protector control scheme introduced for the linear case in a previous work to a class of nonlinear systems. The systems considered are assumed to have a finite propagation velocity while the initial state is subject to a spreading disturbance. We characterize such a control first by using the remediability approach to the resulting nonlinear delay system, and then by coupling families of transformations and the delay approach. To illustrate this work, we provide a...
Relationship between the selection pressure and the rate of mutation accumulation
We use the diploid, sexual Penna ageing model and its modification with noise and environment fluctuations to analyse the influence of random death on the accumulation of defective genes in the genetic pool of populations evolving under different environmental conditions.
Robust Feedback Control Design for a Nonlinear Wastewater Treatment Model
In this work we deal with the design of the robust feedback control of wastewater treatment system, namely the activated sludge process. This problem is formulated by a nonlinear ordinary differential system. On one hand, we develop a robust analysis when the specific growth function of the bacterium μ is not well known. On the other hand, when also the substrate concentration in the feed stream sin is unknown, we provide an observer of system and propose a design of robust feedback control in...
Semigroup Analysis of Structured Parasite Populations
Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which describes the evolution of such a population is a first-order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral...
Sensitivity studies of pollutant concentrations calculated by the UNI-DEM with respect to the input emissions
The influence of emission levels on the concentrations of four important air pollutants (ammonia, ozone, ammonium sulphate and ammonium nitrate) over three European cities (Milan, Manchester, and Edinburgh) with different geographical locations is considered. Sensitivity analysis of the output of the Unified Danish Eulerian Model according to emission levels is provided. The Sobol’ variance-based approach for global sensitivity analysis has been applied to compute the corresponding sensitivity measures....
Sensor network design for the estimation of spatially distributed processes
In a typical moving contaminating source identification problem, after some type of biological or chemical contamination has occurred, there is a developing cloud of dangerous or toxic material. In order to detect and localize the contamination source, a sensor network can be used. Up to now, however, approaches aiming at guaranteeing a dense region coverage or satisfactory network connectivity have dominated this line of research and abstracted away from the mathematical description of the physical...
Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting using Variational Iteration Method
Due to wide range of interest in use of bio-economic models to gain insight into the scientific management of renewable resources like fisheries and forestry,variational iteration method (VIM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting.The results are compared with the results obtained by Adomian decomposition method and reveal that VIM is very effective and convenient for solving nonlinear differential equations.
Some mathematical problems arising in heterogeneous insular ecological models.
En esta nota se analizan dos modelos matemáticos deterministas planteados en problemas ecológicos causados por la introducción de nuevas especies en ambientes insulares heterogéneos. En el primero desarrollamos un modelo epidemológico con transmisión indirecta del virus por medio del ambiente. En el segundo se introduce un modelo específico de depredador-presa que exhibe la extinción en tiempo finito de las especies. Ambos modelos involucran sistemas de ecuaciones en derivadas parciales con interesantes...
Some tracks in air pollution modelling and simulation.
In this article we discuss some issues related to Air Pollution modelling (as viewed by the authors): subgrid parametrization, multiphase modelling, reduction of high dimensional models and data assimilation. Numerical applications are given with POLAIR, a 3D numerical platform devoted to modelling of atmospheric trace species.
Spatial stochastic predator-prey models
We consider a broad class of stochastic lattice predator-prey models whose main features are overviewed. In particular, this article aims at drawing a picture of the influence of spatial fluctuations, which are not accounted for by the deterministic rate equations, on the properties of the stochastic models. Here, we outline the robust scenario obeyed by most of the lattice predator-prey models with an interaction à la Lotka-Volterra. We also show how a drastically different behavior can emerge...
Spatiotemporal Dynamics in a Spatial Plankton System
In this paper, we investigate the complex dynamics of a spatial plankton-fish system with Holling type III functional responses. We have carried out the analytical study for both one and two dimensional system in details and found out a condition for diffusive instability of a locally stable equilibrium. Furthermore, we present a theoretical analysis of processes of pattern formation that involves organism distribution and their interaction of spatially...
Stability analysis of stochastic Ricker population model,.
Stability and bifurcation of numerical discretization Nicholson blowflies equation with delay.
Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites
For an SI type endemic model with one host and two parasite strains, we study the stability of the endemic coexistence equilibrium, where the host and both parasite strains are present. Our model, which is a system of three ordinary differential equations, assumes complete cross-protection between the parasite strains and reduced fertility and increased mortality of infected hosts. It also assumes that one parasite strain is exclusively vertically...
Stability of the positive point of equilibrium of Nicholson's blowflies equation with stochastic perturbations: numerical analysis.
Statistical estimation of the dynamics of watershed dams
In the present study the notion of watershed contour dynamics, defined within the framework of mathematical morphology, is examined. It is shown that the dynamics are a direct measure of the “sharpness” of transition between neighboring watershed basins. The expressions for the expected value and the statistical error of the estimation of contour dynamics are derived in the presence of noise, based on extreme value theory. The sensitivity of contour dynamics to noise is studied. A statistical approach...
Stochastic effects on biodiversity in cyclic coevolutionary dynamics
Finite-size fluctuations arising in the dynamics of competing populations may have dramatic influence on their fate. As an example, in this article, we investigate a model of three species which dominate each other in a cyclic manner. Although the deterministic approach predicts (neutrally) stable coexistence of all species, for any finite population size, the intrinsic stochasticity unavoidably causes the eventual extinction of two of them.
Stochastic equation of population dynamics of prey-predator type with diffusion in a territory.