MONITORING ENVIRONMENTAL CHANGE IN AN ECOSYSTEM

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

Dinamikus rendszerek kvalitatív és kvantitatív tulajdonságainak vizsgálata és alkalmazásai = Applications and analysis of time varying systems

A lineáris rendszerek algebrai vizsgálata kapcsán bevezetett ún. vertikuum-típusú rendszerek segítségével sikerült igen bonyolult gráfú komplex gazdasági és műszaki rendszereket „egyszerűbb szerkezetűvé” transzformálni. A különféle vertikuum-típusú rendszerek mind gyakorlati, mind elméleti jelentősége abban rejlik, hogy egy természetes algoritmizálást kínál, másrészt az is kiderült, hogy „szinte minden” rendszer vertikuum-típusú rendszerré transzformálható. A kutatás során fontos eredmény volt, hogy a részvertikuumok irányíthatósága, megfigyelhetősége és a teljes rendszer irányíthatósága és megfigyelhetősége közötti kapcsolat, amely szerint ha a részvertikuumok megfigyelhetőek és/vagy irányíthatóak, akkor a teljes rendszer is megfigyelhető és/vagy irányítható. A vertikuum-típusú rendszerek vizsgálatakor felmerülő fontos probléma, ha az egyik Ai-t alrendszert ki-, vagy bekapcsoljuk. Egy ilyen rendszer irányíthatóságára adtunk rangfeltételt a kapcsolásokra feltett gerjesztési feltételek mellett, és ezután általánosítottuk több alrendszerre is, valamint sikerült a kapcsolt vertikuum típusú rendszerek irányíthatóságára és megfigyelhetőségére szükséges és elégséges feltételt adnunk. A kutatási tervben szereplő alkalmazásokat illetően egyfelől teljes mértékben teljesítettük a kitűzött kutatási feladatokat, másrészt azokat csatlakozó tematikával sikerült messzemenően kiterjeszteni, és új kontrollelméleti és játékelméleti modellezési vizsgálatokkal kiegészíteni. | Verticuum type systems were introduced during the algebraic analysis of linear systems, and proved to be an excellent means of transforming complex graphed economic and engineering systems to a simpler structure. The theoretical and practical significance of verticuum type systems is that on the one hand almost all systems can be transformed to a verticuum-type representation, and that they offer a straightforward algorithmic approach. An important result of our resarch was that a connection was made between the subverticuums and the original verticuum type systems controllability and observability qualities. We showed that if the subverticuums are observable and/or controllable then the original system is also observable and/or controllable. Concerning another important problem, the switching (on or off) type of subsystems we gave a rank condition for the controllability of the system under given persisting conditions made for the switching subsystem, and we generalised the results for multiple subsystems. Considering the applications outlined in the research plan we managed to fully perform the planned tasks, moreover with the thematical extensions we managed to make a much wider outreach by undertaking additional game theoretical and control theoretical analyses

Observer design for open and closed trophic chains

Monitoring of ecological systems is one of the major issues in ecosystem research. The concepts and methodology of mathematical systems theory provide useful tools to face this problem. In many cases, state monitoring of a complex ecological system consists in observation (measurement) of certain state variables, and the whole state process has to be determined from the observed data. The solution proposed in the paper is the design of an observer system, which makes it possible to approximately recover the state process from its partial observation. Such systems-theoretical approach has been applied before by the authors to Lotka–Volterra type population systems. In the present paper this methodology is extended to a non-Lotka–Volterra type trophic chain of resource–producer–primary consumer type and numerical examples for different observation situations are also presented

VERTICUM-TYPE SYSTEMS APPLIED TO ECOLOGICAL MONITORING

In the paper ecological interaction chains of the type resource – producer – primary user – secondary consumer are considered. 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 introduced for the study of industrial verticums. Applying the technique of such systems, for the monitoring of the considered ecological system, an observer system is constructed, which makes it possible to recover the whole state process from the partial observation of the ecological interaction chain

Proposal for Territorial Management Associated Complex Ecological Lagoon Carimagua, From an Assessment of Ecosystem Services: Municipality of Port Gaitan -Meta

Resumen El complejo ecológico asociado a la laguna Carimagua localizada en el departamento del Meta, Colombia es considerada una estrella fluvial de importancia binacional asociada al a cuenca del Orinoco. Está zona se caracteriza por la prestación de servicios ecosistémicos de gran importancia para garantizar la sostenibilidad de las comunidades, los cuales fueron evaluados desde los componentes social, ecológico y económico con el fin de generar un mecanismos de gestión territorial fundamentado en la relación socioecosistémica buscando la Conservación de la zona mediante la propuesta de creación de un área protegida en el marco del decreto 2372 de 2010 bajo la categoría de Distrito de manejo integrado. Abstract The ecological complex associated Carimagua lagoon located in the department of Meta, Colombia is considered an important binational waterway star associated to the Orinoco basin. It's area is characterized by the provision of ecosystem services important to ensure the sustainability of communities, which were evaluated from the social, ecological and economic components in order to generate mechanisms of territorial management based on the socioecosistemic relationship seeking conservation area through the proposed establishment of a protected area in under the decree 2372 of 2010 under the category of integrated management District area