In this paper the concept of a nonlinear verticumtype observation system is introduced. These systems are composed from several ＂subsystems＂ connected sequentially in a particular way： a part of the state variables...In this paper the concept of a nonlinear verticumtype observation system is introduced. These systems are composed from several ＂subsystems＂ connected sequentially in a particular way： a part of the state variables of each ＂subsystem＂ also appears in the next ＂subsystem＂ as an ＂exogenous variable＂ which can also be interpreted as a con trol generated by an ＂exosystem＂. Therefore these ＂subsystems＂ are not observation systems, but formally can be considered as controlobservation systems. The problem of observability of such systems can be reduced to rank conditions on the ＂subsystems＂. Indeed, under the condition of Lyapunov stability of an equilibrium of the ＂large＂, verticumtype system, it is shown that the Kalman rank condition on the linearization of the ＂subsystems＂ implies the observability of the original, nonlinear verticumtype system. For an illustration of the above linearization result, a stagestructured fishery model with reserve area is considered. Observability for this system is obtained by applying the above linearization and decomposition approach. Furthermore, it is also shown that, applying an appropriate observer design method to each subsystem, from the observa tion of the biomass densities of the adult （harvested） stage, in both areas, the biomass densities of the prerecruit stage can be efficiently estimated.展开更多
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 r...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.展开更多
文摘In this paper the concept of a nonlinear verticumtype observation system is introduced. These systems are composed from several ＂subsystems＂ connected sequentially in a particular way： a part of the state variables of each ＂subsystem＂ also appears in the next ＂subsystem＂ as an ＂exogenous variable＂ which can also be interpreted as a con trol generated by an ＂exosystem＂. Therefore these ＂subsystems＂ are not observation systems, but formally can be considered as controlobservation systems. The problem of observability of such systems can be reduced to rank conditions on the ＂subsystems＂. Indeed, under the condition of Lyapunov stability of an equilibrium of the ＂large＂, verticumtype system, it is shown that the Kalman rank condition on the linearization of the ＂subsystems＂ implies the observability of the original, nonlinear verticumtype system. For an illustration of the above linearization result, a stagestructured fishery model with reserve area is considered. Observability for this system is obtained by applying the above linearization and decomposition approach. Furthermore, it is also shown that, applying an appropriate observer design method to each subsystem, from the observa tion of the biomass densities of the adult （harvested） stage, in both areas, the biomass densities of the prerecruit stage can be efficiently estimated.
文摘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.
