scholarly journals Null Controllability of a Nonlinear Dissipative System and Application to the Detection of the Incomplete Parameter for a Nonlinear Population Dynamics Model

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Yacouba Simporé ◽  
Oumar Traoré
Keyword(s):  
Population Dynamics ◽  
Nonlinear System ◽  
Source Term ◽  
Dissipative System ◽  
Null Controllability ◽  
Dynamics Model ◽  
Carleman Inequality ◽  
Controllability Problem ◽  
Population Dynamics Model ◽  
Controllability Result

We first prove a null controllability result for a nonlinear system derived from a nonlinear population dynamics model. In order to tackle the controllability problem we use an adapted Carleman inequality. Next we consider the nonlinear population dynamics model with a source term called the pollution term. In order to obtain information on the pollution term we use the method of sentinel.

scholarly journals Boundary Null Controllability With Constrained Control for a Nonlinear Two Stroke System: Application to Boundary Sentinel and Identification of Parameters in a Nonlinear Population Dynamics Model

2019 ◽  
Vol 11 (4) ◽  
pp. 51
Author(s):  
Somdouda Sawadogo ◽  
Mifiamba Soma
Keyword(s):  
Population Dynamics ◽  
Incomplete Data ◽  
Null Controllability ◽  
Constrained Control ◽  
Dynamics Model ◽  
Carleman Inequality ◽  
Controllability Problem ◽  
Unknown Parameters ◽  
Population Dynamics Model ◽  
Controllability Result

We first prove a new controllability result for a nonlinear two stroke system. The key to solve this controllability problem is an adapted Carleman inequality. Next, the obtained result is used to build a boundary sentinel to identify unknown parameters in a nonlinear population dynamics model with incomplete data.

scholarly journals Null controllability of a nonlinear population dynamics problem

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
Oumar Traore
Keyword(s):  
Population Dynamics ◽  
Internal Control ◽  
Initial Density ◽  
Adjoint System ◽  
Null Controllability ◽  
Dynamics Model ◽  
Carleman Inequality ◽  
Recruitment Process ◽  
Open Set ◽  
Population Dynamics Model

We establish a null controllability result for a nonlinear population dynamics model. In our model, the birth term is nonlocal and describes the recruitment process in newborn individuals population. Using a derivation of Leray-Schauder fixed point theorem and Carleman inequality for the adjoint system, we show that for all given initial density, there exists an internal control acting on a small open set of the domain and leading the population to extinction.

scholarly journals Boundary Sentinel with Given Sensitivity in Population Dynamics Problem and Parameters Identification

2019 ◽  
Vol 12 (3) ◽  
pp. 1277-1296
Author(s):  
Mifiamba Soma ◽  
Somdouda Sawadogo
Keyword(s):  
Population Dynamics ◽  
Parabolic Equation ◽  
General Framework ◽  
Exact Controllability ◽  
The State ◽  
Parameters Identification ◽  
Dynamics Model ◽  
Carleman Inequality ◽  
Controllability Problem ◽  
Population Dynamics Model

The notion of sentinels with given sensitivity was introduced by J.L.Lions [11] in order to identify parameters in the problem of pollution ruled by a parabolic equation. He proves that the existence of such sentinels is reduced to the solution of exact controllability problem with constraints on the state. In population dynamics model, we reconsider this notion of sentinels in a more general framework. We prove the existence of the boundary sentinels by solving a boundarynull-controllability problem with constraint on the control. Our results use Carleman inequality which is adapted to the constraint.

scholarly journals Simultaneous Null Controllability for Two Stroke Nonlinear Systems: Application to the Sentinel of Detection in Population Dynamics Model with Incomplete Data

2019 ◽  
Vol 12 (3) ◽  
pp. 870-892
Author(s):  
Cédric Kpèbbèwèwèrè Some ◽  
Somdouda Sawadogo
Keyword(s):  
Population Dynamics ◽  
Fixed Point ◽  
Incomplete Data ◽  
Fixed Point Theorems ◽  
Coupled System ◽  
Null Controllability ◽  
Dynamics Model ◽  
Carleman Inequality ◽  
Change Of Variables ◽  
Population Dynamics Model

This paper deals with the simultaneous null controllability for some nonlinear two stroke systems. We shall solve this problem by transforming the simultaneous null controllability of uncoupled initial systems into a null controllability of a coupled system via a change of variables. This last problem is solved thanks to a global Carleman inequality, appropriates estimates adapted to the system and via some fixed point theorems. The obtained results are used to build a simultaneous sentinel of detection in a population dynamics model with incomplete data.

scholarly journals Null Controllability of a Four Stage and Age-Structured Population Dynamics Model

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Amidou Traoré ◽  
Bedr’Eddine Ainseba ◽  
Oumar Traoré
Keyword(s):  
Population Dynamics ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Null Controllability ◽  
Dynamics Model ◽  
Female Population ◽  
Structured Population ◽  
Population Dynamics Model ◽  
Structured Population Dynamics ◽  
Age Structured

This paper is devoted to study the null controllability properties of a population dynamics model with age structuring and nonlocal boundary conditions. More precisely, we consider a four-stage model with a second derivative with respect to the age variable. The null controllability is related to the extinction of eggs, larvae, and female population. Thus, we estimate a time T to bring eggs, larvae, and female subpopulation density to zero. Our method combines fixed point theorem and Carleman estimate. We end this work with numerical illustrations.

scholarly journals Null controllability of a nonlinear age, space and two-sex structured population dynamics model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yacouba Simporé ◽  
Oumar Traoré
Keyword(s):  
Population Dynamics ◽  
Null Controllability ◽  
Auxiliary System ◽  
Dynamics Model ◽  
System A ◽  
Structured Population ◽  
Population Dynamics Model ◽  
Structured Population Dynamics ◽  
Males And Females ◽  
Controllability Problems

<p style='text-indent:20px;'>In this paper, we study the null controllability of a nonlinear age, space and two-sex structured population dynamics model. This model is such that the nonlinearity and the couplage are at birth level. We consider a population with males and females and we are dealing with two cases of null controllability problems.</p><p style='text-indent:20px;'>The first problem is related to the total extinction, which means that, we estimate a time <inline-formula><tex-math id="M1">\begin{document}$ T $\end{document}</tex-math></inline-formula> to bring the male and female subpopulation density to zero. The second case concerns null controllability of male or female subpopulation. Since the absence of males or females in the population stops births; so, if we have the total extinction of the females at time <inline-formula><tex-math id="M2">\begin{document}$ T, $\end{document}</tex-math></inline-formula> and if <inline-formula><tex-math id="M3">\begin{document}$ A $\end{document}</tex-math></inline-formula> is the life span of the individuals, at time <inline-formula><tex-math id="M4">\begin{document}$ T+A $\end{document}</tex-math></inline-formula> one will get certainly the total extinction of the population. Our method uses first an observability inequality related to the adjoint of an auxiliary system, a null controllability of the linear auxiliary system, and after the Schauder's fixed point theorem.</p>

scholarly journals A random effects population dynamics model based on proportions-at-age and removal data for estimating total mortality

2012 ◽  
Vol 69 (11) ◽  
pp. 1881-1893 ◽  
Author(s):  
Verena M. Trenkel ◽  
Mark V. Bravington ◽  
Pascal Lorance
Keyword(s):  
Population Dynamics ◽  
Random Effects ◽  
Fixed Effects ◽  
Random Effect ◽  
Total Mortality ◽  
Estimation Bias ◽  
Effective Sample Size ◽  
Dynamics Model ◽  
Population Dynamics Model ◽  
Study Parameter

Catch curves are widely used to estimate total mortality for exploited marine populations. The usual population dynamics model assumes constant recruitment across years and constant total mortality. We extend this to include annual recruitment and annual total mortality. Recruitment is treated as an uncorrelated random effect, while total mortality is modelled by a random walk. Data requirements are minimal as only proportions-at-age and total catches are needed. We obtain the effective sample size for aggregated proportion-at-age data based on fitting Dirichlet-multinomial distributions to the raw sampling data. Parameter estimation is carried out by approximate likelihood. We use simulations to study parameter estimability and estimation bias of four model versions, including models treating mortality as fixed effects and misspecified models. All model versions were, in general, estimable, though for certain parameter values or replicate runs they were not. Relative estimation bias of final year total mortalities and depletion rates were lower for the proposed random effects model compared with the fixed effects version for total mortality. The model is demonstrated for the case of blue ling (Molva dypterygia) to the west of the British Isles for the period 1988 to 2011.

A microbial treatment population dynamics optimization approach

2021 ◽  
pp. 1-15
Author(s):  
Jinding Gao
Keyword(s):  
Population Dynamics ◽  
Information Exchange ◽  
Information Diffusion ◽  
Optimization Problems ◽  
Microbial Control ◽  
Function Optimization ◽  
Optimization Approach ◽  
Dynamics Model ◽  
Population Dynamics Model ◽  
Number Of Individuals

In order to solve some function optimization problems, Population Dynamics Optimization Algorithm under Microbial Control in Contaminated Environment (PDO-MCCE) is proposed by adopting a population dynamics model with microbial treatment in a polluted environment. In this algorithm, individuals are automatically divided into normal populations and mutant populations. The number of individuals in each category is automatically calculated and adjusted according to the population dynamics model, it solves the problem of artificially determining the number of individuals. There are 7 operators in the algorithm, they realize the information exchange between individuals the information exchange within and between populations, the information diffusion of strong individuals and the transmission of environmental information are realized to individuals, the number of individuals are increased or decreased to ensure that the algorithm has global convergence. The periodic increase of the number of individuals in the mutant population can greatly increase the probability of the search jumping out of the local optimal solution trap. In the iterative calculation, the algorithm only deals with 3/500∼1/10 of the number of individual features at a time, the time complexity is reduced greatly. In order to assess the scalability, efficiency and robustness of the proposed algorithm, the experiments have been carried out on realistic, synthetic and random benchmarks with different dimensions. The test case shows that the PDO-MCCE algorithm has better performance and is suitable for solving some optimization problems with higher dimensions.

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