Verticum-type systems applied to ecological monitoring

Gámez, Manuel; López, Inmaculada; Szabó, István; Varga, Zoltán

doi:10.1016/j.amc.2009.10.010

Cited by 5 publications

(8 citation statements)

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“…In fact, population interactions are typically nonlinear, but in Gámez et al (2010) an ecological interaction chain of the type resource -producer -primary user -secondary consumer turned out to have a verticum-like structure which admitted to reduce the monitoring (observability) problem to a linearized version of the original model. In Molnár et al (2012), the concept of a nonlinear verticum-type observation system has been introduced, and a decomposition of the sufficient condition for observability of such systems have been proved.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium control of nonlinear verticum-type systems, applied to integrated pest control

et al. 2013

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Linear verticum-type control and observation systems have been introduced for modelling certain industrial systems, consisting of subsystems, vertically connected by certain state variables. Recently the concept of verticum-type observation systems and the corresponding observability condition have been extended by the authors to the nonlinear case. In the present paper the general concept of a nonlinear verticum-type control system is introduced, and a sufficient condition for local controllability to equilibrium is obtained. In addition to a usual linearization, the basic idea is a decomposition of the control of the whole system into the control of the subsystems. Starting from the integrated pest control model of Rafikov and E.H. Limeira (2012) a nonlinear verticum-type model has been set up an equilibrium control is obtained. Furthermore, a corresponding bioeconomical problem is solved minimizing the total cost of integrated pest control (combining chemical control with a biological one).

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Section: Introductionmentioning

confidence: 99%

Equilibrium control of nonlinear verticum-type systems, applied to integrated pest control

et al. 2013

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“…In Section 2, based on [42], following a necessary stability analysis according to [43], the stock estimation of a fish population with reserved area is presented, using an appropriate observer design. In Section 3 results from [40] are recalled concerning the monitoring of ecological interaction chains of the type resource-producer-primary user-secondary consumer. The dynamic behaviour of these four-level chains is modelled by a system of differential equations, the linearization of which is a verticum-type system.…”

Section: Introduction and Historical Overviewmentioning

confidence: 99%

“…The problem of observability of such systems can be reduced to rank conditions on the "subsystems", which is a kind of decoupling of a complex system into simpler parts. Since most dynamic models of population biology are nonlinear, for the application in this field, it was necessary to extend the basic concepts and theorems of the theory of linear verticumtype systems to the nonlinear case, which has been done recently in [19,[39][40][41].…”

Section: Introduction and Historical Overviewmentioning

confidence: 99%

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Recent Developments in Monitoring of Complex Population Systems

Varga

Gámez

López

2013

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The paper is an update of two earlier review papers concerning the application of the methodology of mathematical systems theory to population ecology, a research line initiated two decades ago. At the beginning the research was concentrated on basic qualitative properties of ecological models, such as observability and controllability. Observability is closely related to the monitoring problem of ecosystems, while controllability concerns both sustainable harvesting of population systems and equilibrium control of such systems, which is a major concern of conservation biology. For population system, observability means that, e.g. from partial observation of the system (observing only certain indicator species), in principle the whole state process can be recovered. Recently, for different ecosystems, the so-called observer systems (or state estimators) have been constructed that enable us to effectively estimate the whole state process from the observation. This technique offers an efficient methodology for monitoring of complex ecosystems (including spatially and stage-structured population systems). In this way, from the observation of a few indicator species the state of the whole complex system can be monitored, in particular certain abiotic effects such as environmental contamination can be identified. In this review, with simple and transparent examples, three topics illustrate the recent developments in monitoring methodology of ecological systems: stock estimation of a fish population with reserve area; and observer construction for two vertically structured population systems (verticum-type systems): a four-level ecological chain and a stage-structured fishery model with reserve area.

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“…Such systems are 20 hierarchically composed of subsystems such that a part of the state variables of each subsystem 21 affect the dynamics of the next subsystem. Systems-theoretical properties of such systems were 22 studied in Molnár (1993), Molnár and Szigeti (1994), Gámez et al (2010), and for the 23 monitoring problem of nonlinear verticum-type population systems see Molnár et al (2012). 24…”

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A two-agent model applied to the biological control of the sugarcane borer (Diatraea saccharalis) by the egg parasitoid Trichogramma galloi and the larvae parasitoid Cotesia flavipes

et al. 2016

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Abstract. The paper is aimed at a methodological development in biological pest control. The 10 considered one pest two-agent system is modelled as a verticum-type system. Originally, linear 11 verticum-type systems were introduced by one of the authors for modelling certain industrial 12 systems. These systems are hierarchically composed of linear subsystems such that a part of the 13 state variables of each subsystem affect the dynamics of the next subsystem. Recently, 14 verticum-type system models have been applied to population ecology as well, which required 15 the extension of the concept a verticum-type system to the nonlinear case. 16In the present paper the general concepts and technics of nonlinear verticum-type control 17 systems are used to obtain biological control strategies in a two-agent system. For the 18 illustration of this verticum-type control, these tools of mathematical systems theory are applied 19 to a dynamic model of interactions between the egg and larvae populations of the sugarcane 20 borer (Diatraea saccharalis) and its parasitoids: the egg parasitoid Trichogramma galloi and the 21 larvae parasitoid Cotesia flavipes. 22In this application a key role is played by the concept of controllability, which means that it is 23 possible to steer the system to an equilibrium in given time. In addition to a usual linearization, 24 the basic idea is a decomposition of the control of the whole system into the control of the 25 subsystems, making use of the verticum structure of the population system. The main aim of 26 this study is to show several advantages of the verticum (or decomposition) approach over the 27 classical control theoretical model (without decomposition). For example, in the case of 28 verticum control the pest larval density decreases below the critical threshold value much 29 quicker than without decomposition. Furthermore, it is also shown that the verticum approach 30 may be better even in terms of cost effectiveness. The presented optimal control methodology 31 also turned out to be an efficient tool for the "in silico" analysis of the cost-effectiveness of 32 different biocontrol strategies, e.g. by answering the question how far it is cost-effective to 33 speed up the reduction of the pest larvae density, or along which trajectory this reduction should 34 be carried out. 35 36

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Verticum-type systems applied to ecological monitoring

Cited by 5 publications

References 9 publications

Equilibrium control of nonlinear verticum-type systems, applied to integrated pest control

Equilibrium control of nonlinear verticum-type systems, applied to integrated pest control

Recent Developments in Monitoring of Complex Population Systems

A two-agent model applied to the biological control of the sugarcane borer (Diatraea saccharalis) by the egg parasitoid Trichogramma galloi and the larvae parasitoid Cotesia flavipes

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