State monitoring of a population system in changing environment

Varga, Zoltán; Scarelli, Antonino; Shamandy, A.

doi:10.1556/comec.4.2003.1.11

Cited by 19 publications

(17 citation statements)

References 9 publications

(7 reference statements)

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“…For earlier applications of the concept of observability and observer systems, see e.g. Varga et al (2003), López et al (2007), Varga (2008) and Gámez et al (2008). In Section 4 with illustrative data we will show how the number of healthy cells can be steered to a desired level, applying an appropriate feedback control.…”

Section: Introductionmentioning

confidence: 99%

Observation and control in a model of a cell population affected by radiation

et al. 2009

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The effect of radiation on a cell population is described by a two-dimensional nonlinear system of differential equations. If the radiation rate is not too high, the system is known to have an asymptotically stable equilibrium. First, for the monitoring of this effect, the concept of observability is applied. For the case when the total number of cells is observed, without distinction between healthy and affected cells, a so-called observer system is constructed, which, at least near the equilibrium state, makes it possible to recover the dynamics of both the healthy and the affected cells, from the observation of the total number of cells without distinction.Results of simulations with illustrative data are also presented. If we want to control the system into a required new equilibrium state, and maintain this new equilibrium by a constant control, a technique of theory of optimal control can be applied to construct a feedback control system.

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Section: Introductionmentioning

confidence: 99%

Observation and control in a model of a cell population affected by radiation

et al. 2009

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“…The methodological foundations of the application of controllability and observability to frequency-dependent population models (described by systems with invariant manifold), have been set in Varga (1989) and Varga (1992), see also Scarelli and Varga (2002). The original problem of state monitoring of a population system as formulated in Varga et al (2003) is that, from the observation of the time-dependent densities of certain species, the whole state process of the population system is to be recovered. An important concept for the solution of this problem is observability.…”

Section: Introductionmentioning

confidence: 99%

“…The latter in this context means that from the observation of one or several (but not all) state variables, it is possible to recover the whole state process of the populations system, in a unique way (without determining, however, a constructive method to obtain this process.) Observability has been analysed in different population system models in Varga et al (2002Varga et al ( , 2003 and Shamandy (2005), see also López (2003), López et al (2004). In order to prove observability, we use a general sufficient condition for local observability of nonlinear observation systems, published in Lee and Markus (1971).…”

Section: Introductionmentioning

confidence: 99%

Monitoring environmental change in an ecosystem

Gámez¹,

López²,

Molnár³

2008

Biosystems

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Abstract:The monitoring and analysis of the processes taking place in an ecosystem is a key issue for a sustainable human activity. A system of populations, as the biotic component of a complex ecosystem is usually affected by the variation of its abiotic environment. Even in nearly natural ecosystems an abiotic effect like climatic implications of global warming may cause important changes in the dynamics of the population system. In ecosystems involving field cultivation or any industrial activity; the abiotic parameter in question may be the concentration of a substance, changing e.g. as a result of pollution, application of a pesticide, or a fertilizer, etc. In many cases the observation of the densities of each population may be technically complicated or expensive, therefore the question arises whether from the observation of the densities of certain (indicator) populations, the whole state process of the population system can be uniquely recovered. The paper is aimed at a methodological development of the state monitoring, under the conditions of a changing environment. It is shown, how the technique of mathematical systems theory can be applied not only for the approximate calculation of the state process on the basis of the observed data, even under the effect of an exogene abiotic change with known dynamics; but in certain cases, also for the estimation of the unknown biological effect of the change of an abiotic parameter. The proposed methodology is applied to simple illustrative examples concerning a three-species predator-prey system.

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“…The corresponding concepts 29 and theorems have been extended with local character to nonlinear systems in [3], but 30 found applications to population systems only recently, see e.g. [4]- [10]. These papers 31 either deal with the theoretical problem of observability or, if also observers are 32 constructed, the results concern only Lotka-Volterra-type population systems.…”

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confidence: 99%

“…4), where all components are present. The right-3 hand side of the system is given by the following function: …”

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Verticum-type systems applied to ecological monitoring

Gámez

López

Szabó

et al. 2010

Applied Mathematics and Computation

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Abstract. In the paper ecological interaction chains of the type resource -producer -11 primary user -secondary consumer are considered. The dynamic behaviour of these 12 four-level chains is modelled by a system of differential equations, the linearization of 13 which is a verticum-type systems introduced for the study of industrial verticums.14 Applying the technique of such systems, for the monitoring of the considered ecological 15 system, an observer system is constructed, which makes it possible to recover the whole 16 state process from the partial observation of the ecological interaction chain.

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State monitoring of a population system in changing environment

Cited by 19 publications

References 9 publications

Observation and control in a model of a cell population affected by radiation

Observation and control in a model of a cell population affected by radiation

Monitoring environmental change in an ecosystem

Verticum-type systems applied to ecological monitoring

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