共查询到20条相似文献,搜索用时 15 毫秒
1.
In this article we consider a size structured population model with a nonlinear growth rate depending on the individual's size and on the total population. Our purpose is to take into account the competition for a resource (as it can be light or nutrients in a forest) in the growth of the individuals and study the influence of this nonlinear growth in the population dynamics. We study the existence and uniqueness of solutions for the model equations, and also prove the existence of a (compact) global attractor for the trajectories of the dynamical system defined by the solutions of the model. Finally, we obtain sufficient conditions for the convergence to a stationary size distribution when the total population tends to a constant value, and consider some simple examples that allow us to know something about their global dynamics.This work was partially supported by DGICYT PB90-0730-C02-01 and PB91-0497. 相似文献
2.
Helen M. Byrne 《Journal of mathematical biology》1999,39(1):59-89
In this paper we study a mathematical model that describes the growth of an avascular solid tumour. Our analysis concentrates
on the stability of steady, radially-symmetric model solutions with respect to perturbations taken from the class of spherical
harmonics. Using weakly nonlinear analysis, previous results are extended to show how the amplitudes of the asymmetric modes
interact. Attention focuses on a special case for which the model equations simplify. Analysis of the simplified model equations
leads to the identification of a two-parameter family of asymmetric steady solutions, the dimensions of whose stable and unstable
manifolds depend on the system parameters. The asymmetric steady solutions limit the basin of attraction of the radially-symmetric
steady state when it is linearly stable. On the basis of these numerical and analytical results we postulate the existence
of fully nonlinear steady solutions which are stable with respect to time-dependent perturbations.
Received: 25 October 1998 / Revised version: 20 June 1998 相似文献
3.
Raymond P. Canale 《Biotechnology and bioengineering》1970,12(3):353-378
Mathematical models of the interaction between predator and host populations have been expressed as systems of nonlinear ordinary differential equations. Solutions of such systems may be periodic or aperiodic. Periodic, oscillatory solutions may depend on the initial conditions of the system or may be limit cycles. Aperiodic solutions can, but do not necessarily, exhibit oscillatory behavior. Therefore, it is important to characterize predatory-prey models on the basis of the possible types of solutions they may possess. This characterization can be accomplished using some well-known methods of nonlinear analysis. Examination of the system singular points and inspection of phase plane portraits have proved to be useful techniques for evaluating the effect of various modifications of early predator-prey models. Of particular interest is the existence of limit cycle oscillations in a model in which predator growth rate is a function of the concentration of prey. 相似文献
4.
N Kato 《Journal of biological dynamics》2012,6(Z1):42-53
We study stationary solutions to a system of size-structured population models with nonlinear growth rate. Several characterizations of stationary solutions are provided. It is shown that the steady-state problem can be converted into different problems such as two types of eigenvalue problems and a fixed-point problem. In the two-species case, we give an existence result of nonzero stationary solutions by using the fixed-point problem. 相似文献
5.
This paper develops the mathematical analysis of nonlinear boundary-value problems that model the facilitated diffusion of a substrate across a membrane. The analysis includes bounds for solutions, global existence results, local uniqueness and continuity results, and estimates for parameter ranges for uniqueness of solutions. 相似文献
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8.
Travelling waves of a delayed SIR epidemic model with nonlinear incidence rate and spatial diffusion
This paper is concerned with the existence of travelling waves to a SIR epidemic model with nonlinear incidence rate, spatial diffusion and time delay. By analyzing the corresponding characteristic equations, the local stability of a disease-free steady state and an endemic steady state to this system under homogeneous Neumann boundary conditions is discussed. By using the cross iteration method and the Schauder's fixed point theorem, we reduce the existence of travelling waves to the existence of a pair of upper-lower solutions. By constructing a pair of upper-lower solutions, we derive the existence of a travelling wave connecting the disease-free steady state and the endemic steady state. Numerical simulations are carried out to illustrate the main results. 相似文献
9.
Thenonlinearintegralequation(1.1)isageneralizedmodelforthespreadofdiseaseswithseasonaldependence.Inthispaper,wehaveprovedtheexistenceofatleastthreenontrivialnonnegativeperiodicsolutionstothisequation. 相似文献
10.
A model of bacteria and phage survival is developed based on the idea of shielding by bacterial debris in the system. This model is mathematically formulated by a set of four nonlinear difference equations for susceptible bacteria, contaminated bacteria, bacterial debris and phages. Simulation results show the possibility of survival, and domains of existence of stable and unstable solutions 相似文献
11.
David H. Anderson 《Mathematical biosciences》1984,71(1):105-119
This paper is concerned with the nonlinear system of algebraic equations relating the positive parameters of a linear time-invariant compartmental model to its transfer function coefficients. The general form that these equations must take is shown, and simple necessary conditions for the existence of positive solutions are given. An immediate use of these conditions is the development of necessary conditions for a polynomial with positive coefficients to have negative roots. A method is then outlined which triangularizes the system and reduces the complete solution problem to one of finding and counting roots of a polynomial. Sufficient conditions for the existence of real and positive solutions are demonstrated. 相似文献
12.
Shihe Xu 《Journal of biological dynamics》2017,11(1):504-520
In this paper, the existence, uniqueness and exponential stability of almost periodic solutions for a mathematical model of tumour growth are studied. The establishment of the model is based on the reaction–diffusion dynamics and mass conservation law and is considered with a delay in the cell proliferation process. Using a fixed-point theorem in cones, the existence and uniqueness of almost periodic solutions for different parameter values of the model is proved. Moreover, by the Gronwall inequality, sufficient conditions are established for the exponential stability of the unique almost periodic solution. Results are illustrated by computer simulations. 相似文献
13.
M. N. Oğuztöreli 《Biological cybernetics》1975,18(1):41-48
In this work an attempt is made to study the activities in a continuous neural system. The neural model considered here is a two dimensional continuous version of an earlier discrete model investigated in a series of papers [5–8]. The variations of the normalized firing rates in the present model are described by a nonlinear integro-partial differential equation. The conditions for the existence and uniqueness of the solutions of the describing equation subject to an initial condition are established and the steady-state solutions are investigated for inputs which are constant with respect to time. Depending on the parameters which are related to the self-inhibition and adaptation properties of the neural network, some of the oscillatory and stability properties of the solutions of the describing equation are discussed. 相似文献
14.
Obeyesekere MN Zimmerman SO Tecarro ES Auchmuty G 《Bulletin of mathematical biology》1999,61(5):917-934
A modified version of a previously developed mathematical model [Obeyesekere et al., Cell Prolif. (1997)] of the G1-phase of the cell cycle is presented. This model describes the regulation of the G1-phase that includes the interactions of the nuclear proteins, RB, cyclin E, cyclin D, cdk2, cdk4 and E2F. The effects of
the growth factors on cyclin D synthesis under saturated or unsaturated growth factor conditions are investigated based on
this model. The solutions to this model (a system of nonlinear ordinary differential equations) are discussed with respect
to existing experiments. Predictions based on mathematical analysis of this model are presented. In particular, results are
presented on the existence of two stablesolutions, i. e., bistability within the G1-phase. It is shown that this bistability exists under unsaturated growth factor concentration levels. This phenomenon is
very noticeable if the efficiency of the signal transduction, initiated by the growth factors leading to cyclin D synthesis,
is low. The biological significance of this result as well as possible experimental designs to test these predictions are
presented. 相似文献
15.
A nonlinear relativistic quantum theory of stimulated Cherenkov emission of longitudinal waves by a relativistic monoenergetic
electron beam in a cold isotropic plasma is presented. The theory makes use of a quantum model based on the Klein-Gordon equation.
The instability growth rates are obtained in the linear approximation and are shown to go over to the familiar growth rates
in the classical limit. The mechanisms for the nonlinear saturation of relativistic Cherenkov beam instabilities are described
with allowance for quantum effects, and the corresponding analytic solutions are derived. 相似文献
16.
An equation of growth of a single species with realistic dependence on crowding and seasonal factors
Martino Bardi 《Journal of mathematical biology》1983,17(1):33-43
Various biological phenomena lead to single species models where the relative rate of increase is a non-monotone function of the density, i.e. depensation models. A brief survey of the literature and some new models are given. A nonlinear nonautonomous O.D.E. is proposed as a general depensation model in a periodically fluctuating environment. Results on existence, multiplicity and global stability of periodic solutions are given. 相似文献
17.
Global stability of stationary solutions to a nonlinear diffusion equation in phytoplankton dynamics
We consider a nonlinear diffusion equation proposed by Shigesada and Okubo which describes phytoplankton growth dynamics with a selfs-hading effect.We show that the following alternative holds: Either (i) the trivial stationary solution which vanishes everywhere is a unique stationary solution and is globally stable, or (ii) the trivial solution is unstable and there exists a unique positive stationary solution which is globally stable. A criterion for the existence of positive stationary solutions is stated in terms of three parameters included in the equation. 相似文献
18.
Roger Lui 《Journal of mathematical biology》1983,16(3):199-220
In this paper, we establish the existence and stability property of travelling wave solutions of a nonlinear integral operator in the inferior case. 相似文献
19.
Early development and quorum sensing in bacterial biofilms 总被引:3,自引:0,他引:3
Ward JP King JR Koerber AJ Croft JM Sockett RE Williams P 《Journal of mathematical biology》2003,47(1):23-55
We develop mathematical models to examine the formation, growth and quorum sensing activity of bacterial biofilms. The growth
aspects of the model are based on the assumption of a continuum of bacterial cells whose growth generates movement, within
the developing biofilm, described by a velocity field. A model proposed in Ward et al. (2001) to describe quorum sensing, a process by which bacteria monitor their own population density by the use of quorum
sensing molecules (QSMs), is coupled with the growth model. The resulting system of nonlinear partial differential equations
is solved numerically, revealing results which are qualitatively consistent with experimental ones. Analytical solutions derived
by assuming uniform initial conditions demonstrate that, for large time, a biofilm grows algebraically with time; criteria
for linear growth of the biofilm biomass, consistent with experimental data, are established. The analysis reveals, for a
biologically realistic limit, the existence of a bifurcation between non-active and active quorum sensing in the biofilm.
The model also predicts that travelling waves of quorum sensing behaviour can occur within a certain time frame; while the
travelling wave analysis reveals a range of possible travelling wave speeds, numerical solutions suggest that the minimum
wave speed, determined by linearisation, is realised for a wide class of initial conditions.
Received: 10 February 2002 / Revised version: 29 October 2002 /
Published online: 19 March 2003
Key words or phrases: Bacterial biofilm – Quorum sensing – Mathematical modelling – Numerical solution – Asymptotic analysis – Travelling wave
analysis 相似文献
20.
Kohlmann M 《Acta biotheoretica》2012,60(3):273-287
The present paper deals with a free boundary problem modeling the growth process of necrotic multi-layer tumors. We prove the existence of flat stationary solutions and determine the linearization of our model at such an equilibrium. Finally, we compute the solutions of the stationary linearized problem and comment on bifurcation. 相似文献