Existence and uniqueness of solutions for a diffusion model of host-parasite dynamics

Milner and Patton (J. Comput. Appl. Math., in press) introduced earlier a new approach to modeling host-parasite dynamics through a convection-diffusion partial differential equation, which uses the parasite density as a continuous structure variable. A motivation for the model was presented there, as well as results from numerical simulations and comparisons with those from other models. However, no proof of existence or uniqueness of solutions to the new model proposed was included there. In the present work the authors deal with the well posedness of that model and they prove existence and uniqueness of solutions, as well as establishing some asymptotic results.     

Continuous dependence results for a general model of size-dependent population dynamics

We are concerned with a general model of size structured population dynamics with the growth rate depending on the individual's size and time. In this paper, we shall study the continuous dependence of the solution on all given data such as aging and birth functions, growth rate functions and initial data.     

Existence of positive solutions for a thermostat model

We study a second order nonlinear boundary value problem subject to some nonlocal boundary conditions, which models a thermostat. The sensors are linear functionals, one gives feedback from part of the interval to a controller at one endpoint, the other gives feedback to a controller at the other endpoint. We determine the Green’s function and establish its useful properties which enables us to establish the existence of multiple positive solutions and to prove nonexistence results. We calculate all relevant constants in some explicit examples.     

An age structured population model in a spatially heterogeneous environment: Existence and uniqueness theory

This paper considers the existence and uniqueness of solutions of an age-structured population model in a spatially heterogeneous bounded environment. The model describes individual organism movement of diffusion and advection in the older life stage but assumes stationarity of individuals in the embryonic stage. The mathematical formulation is a nonlinear degenerate parabolic partial differential problem with non-locally integro-type initial-boundary conditions.     

Existence and uniqueness for a stochastic age-structured population system with diffusion

In this paper, a class of stochastic age-dependent population dynamic system with diffusion is introduced. Existence and uniqueness of strong solution for a stochastic age-dependent population dynamic system in Hilbert space are established. The analysis use Barkholder–Davis–Gundy’s inequality, Itô’s formula and some special inequalities for our purposes.     

Existence and uniqueness of mild solutions to a semilinear integrodifferential equation of fractional order

In this paper, we prove some existence and uniqueness of mild solutions for a semilinear integrodifferential equation of fractional order with nonlocal initial conditions in α-norm. We assume that the linear part generates a noncompact analytic semigroup. Our results cover the cases that the nonlinearity F takes values in different spaces such as X,X_α and X_β, where α≤β(0,1). Finally, some practical consequences are also obtained.     

Optimal control for age-structured population dynamics of incomplete data

We are concerned with the control question for linear age-structured population dynamics of incomplete initial data. More precisely, the initial population age distribution is supposed to be unknown. We here generalize the notion of no-regret control of Lions (1992) [10] to such singular population dynamics, following the method by Nakoulima, Omrane and Vélin (2000) [16]. We prove that the problem we are considering has a unique no-regret control that we characterize by a singular optimality system.     

Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal

This paper is concerned with a nonlocal evolution equation which is used to model the spatial dispersal of organisms. We study the existence, uniqueness and stability of the positive steady solution for this nonlocal evolution equation under general conditions. The global dynamics are also investigated and a trichotomy of the global asymptotics is established.     

EXISTENCE AND GLOBAL ATTRACTIVITY OF PERIODIC SOLUTION OF A MODEL IN POPULATION DYNAMICS

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Existence and uniqueness of positive periodic solutions for a neutral Logarithmic population model

In this paper, by using an abstract continuous theorem of k-set contractive operator, the criteria is established for the existence, global attractivity of positive periodic solution of a neutral delay Logarithmic population model with multiple delays. The result improve the known ones in [S.P. Lu, W.G. Ge, Existence of positive periodic solutions for neutral Logarithmic population model with multiple delays, J. Comput. Appl. Math. 166 (2) (2004) 371-383].     

Modelling complex systems in applied sciences; methods and tools of the mathematical kinetic theory for active particles

This paper deals with the modelling of large systems of interacting individuals characterized by a microscopic state which includes both mechanical and socio-biological activities. The first part of the paper is devoted to the derivation and critical analysis of the modelling of microscopic equations and subsequently of the derivation of evolution equations. The second part analyzes how these mathematical structures can be properly used to model a variety of models in different fields of applied sciences: traffic flow, population dynamics, biology. Some research perspectives are analyzed in the last part of the paper.     

A numerical approximation for Volterra’s population growth model with fractional order

This paper presents a numerical scheme for approximate solutions of the fractional Volterra’s model for population growth of a species in a closed system. In fact, the Bessel collocation method is extended by using the time-fractional derivative in the Caputo sense to give solutions for the mentioned model problem. In this extended of the method, a generalization of the Bessel functions of the first kind is used and its matrix form is constructed. And then, the matrix form based on the collocation points is formed for the each term of this model problem. Hence, the method converts the model problem into a system of nonlinear algebraic equations. We give some numerical applications to show efficiency and accuracy of the method. In applications, the reliability of the technique is demonstrated by the error function based on accuracy of the approximate solution.     

Stability and regularity results for a size-structured population model

In the present paper a nonlinear size-structured population dynamical model with size and density dependent vital rate functions is considered. The linearization about stationary solutions is analyzed by semigroup and spectral methods. In particular, the spectrally determined growth property of the linearized semigroup is derived from its long-term regularity. These analytical results make it possible to derive linear stability and instability results under biologically meaningful conditions on the vital rates. The principal stability criteria are given in terms of a modified net reproduction rate.     

Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps

Numerical Algorithms - An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point particles placed in $mathbb {R}^{d} (d geq 1)$ ....     

Population model with diffusion and supplementary forest resource in a two-patch habitat

A mathematical model is proposed to study the role of supplementary self-renewable resource on species population in a two-patch habitat. It is assumed that the density of forest resource biomass is governed by the logistic equation in both the regions but with the different intrinsic growth rate but the same carrying capacity in the entire habitat. It is further assumed that the densities of species population is also governed by the generalized logistic equations in both the regions but with different growth rates and carrying capacities. It is shown that the steady state solutions are positive, monotonic and continuous under both reservoir and no-flux boundary conditions. The linear and non-linear asymptotic stability conditions of non-uniform steady state are compared with the case of the model with and without diffusion in a homogeneous habitat.     

A uniqueness result for a nonlocal equation of Kirchhoff type and some related open problem

We study the uniqueness of solution for the following boundary value problem involving a nonlocal equation of Kirchhoff type

     

Oscillation of partial population model with diffusion and delay

By using the upper- and lower-solution method of partial functional differential equations and the oscillation theory of functional differential equation, the oscillation of a population equation with diffusion and delay is studied and a sufficient condition for all positive solutions of the equation to oscillate about the positive equilibrium is obtained. Finally, a model arising from ecology is given to illustrate the obtained results.     

可化约拟线性双曲组带一类非局部边界条件的精确边界能控性

先证明了一类非线性积分方程解的存在唯一性,利用此结果,建立了可化约拟线性双曲组带一类非局部边界条件的单侧精确边界能控性.