Complex dynamics in simple systems with periodic parameter oscillations

We study systems with periodically oscillating parameters that can give way to complex periodic or nonperiodic orbits. Performing the long time limit, we can define ergodic averages such as Lyapunov exponents, where a negative maximal Lyapunov exponent corresponds to a stable periodic orbit. By this, extremely complicated periodic orbits composed of contracting and expanding phases appear in a natural way. Employing the technique of ϵ-uncertain points, we find that values of the control parameters supporting such periodic motion are densely embedded in a set of values for which the motion is chaotic. When a tiny amount of noise is coupled to the system, dynamics with positive and with negative nontrivial Lyapunov exponents are indistinguishable. We discuss two physical systems, an oscillatory flow inside a duct and a dripping faucet with variable water supply, where such a mechanism seems to be responsible for a complicated alternation of laminar and turbulent phases.

Importance of allelopathy as peudo-mixotrophy for the dynamics and diversity of phytoplankton

Understanding the dynamics and diversity of marine phytoplankton is essential for predicting oceanic primary production, oxygen generation and carbon sequestration. Several top-down and bottom-up factors lead to complex phytoplankton dynamics. Complexities further arise from inter-species interactions within phytoplankton communities. Consequently, some of the basic questions on phytoplankton diversity, identified long ago, still puzzle the ecologists: for example, what regulates the diversity in simple systems where species compete for limiting resources? In this context, allelopathic interaction among phytoplankton species has been identified as a potential driver of their dynamics and regulator of their diversity. This chapter deals with the importance of allelopathy in regulating the outcome of nutrient competition among phytoplankton species, through analysis of a resource-competition model. It demonstrates that, through the mechanism of pseudo-mixotrophy - proposed earlier by the author - allelopathy provides essential growth advantage to weaker competitors, and stabilizes resource competition, which ensures the coexistence of two phytoplankton on a single nutrient. In simple nutrient-phytoplankton interactions where higher-trophic influences are negligible, this mechanism theoretically promotes phytoplankton diversity, and can potentially support high diversity in natural phytoplankton communities.

Sensitivity of large-scale atmospheric analyses to humidity observations and its impact on the global water cycle and tropical and extratropical weather systems in ERA40

Reanalysis data obtained from data assimilation are increasingly used for diagnostic studies of the general circulation of the atmosphere, for the validation of modelling experiments and for estimating energy and water fluxes between the Earth surface and the atmosphere. Because fluxes are not specifically observed, but determined by the data assimilation system, they are not only influenced by the utilized observations but also by model physics and dynamics and by the assimilation method. In order to better understand the relative importance of humidity observations for the determination of the hydrological cycle, in this paper we describe an assimilation experiment using the ERA40 reanalysis system where all humidity data have been excluded from the observational data base. The surprising result is that the model, driven by the time evolution of wind, temperature and surface pressure, is able to almost completely reconstitute the large-scale hydrological cycle of the control assimilation without the use of any humidity data. In addition, analysis of the individual weather systems in the extratropics and tropics using an objective feature tracking analysis indicates that the humidity data have very little impact on these systems. We include a discussion of these results and possible consequences for the way moisture information is assimilated, as well as the potential consequences for the design of observing systems for climate monitoring. It is further suggested, with support from a simple assimilation study with another model, that model physics and dynamics play a decisive role for the hydrological cycle, stressing the need to better understand these aspects of model parametrization. .

Modelling nitrogen fluxes from the land surface to the coastal zone in European systems: the perspective of the INCA project

This paper describes the results and conclusions of the INCA (Integrated Nitrogen Model for European CAtchments) project and sets the findings in the context of the ELOISE (European Land-Ocean Interaction Studies) programme. The INCA project was concerned with the development of a generic model of the major factors and processes controlling nitrogen dynamics in European river systems, thereby providing a tool (a) to aid the scientific understanding of nitrogen transport and retention in catchments and (b) for river-basin management and policy-making. The findings of the study highlight the heterogeneity of the factors and processes controlling nitrogen dynamics in freshwater systems. Nonetheless, the INCA model was able to simulate the in-stream nitrogen concentrations and fluxes observed at annual and seasonal timescales in Arctic, Continental and Maritime-Temperate regimes. This result suggests that the data requirements and structural complexity of the INCA model are appropriate to simulate nitrogen fluxes across a wide range of European freshwater environments. This is a major requirement for the production of coupled fiver-estuary-coastal shelf models for the management of our aquatic environment. With regard to river-basin management, to achieve an efficient reduction in nutrient fluxes from the land to the estuarine and coastal zone, the model simulations suggest that management options must be adaptable to the prevailing environmental and socio-economic factors in individual catchments: 'Blanket approaches' to environmental policy appear too simple. (c) 2004 Elsevier B.V. All rights reserved.

A simple theoretical model for the intensification of tropical cyclones and polar lows

A simple theoretical model for the intensification of tropical cyclones and polar lows is developed using a minimal set of physical assumptions. These disturbances are assumed to be balanced systems intensifying through the WISHE (Wind-Induced Surface Heat Exchange) intensification mechanism, driven by surface fluxes of heat and moisture into an atmosphere which is neutral to moist convection. The equation set is linearized about a resting basic state and solved as an initial-value problem. A system is predicted to intensify with an exponential perturbation growth rate scaled by the radial gradient of an efficiency parameter which crudely represents the effects of unsaturated processes. The form of this efficiency parameter is assumed to be defined by initial conditions, dependent on the nature of a pre-existing vortex required to precondition the atmosphere to a state in which the vortex can intensify. Evaluation of the simple model using a primitive-equation, nonlinear numerical model provides support for the prediction of exponential perturbation growth. Good agreement is found between the simple and numerical models for the sensitivities of the measured growth rate to various parameters, including surface roughness, the rate of transfer of heat and moisture from the ocean surface, and the scale for the growing vortex.

Singular vector ensemble forecasting systems and the prediction of flow dependent uncertainty

The ECMWF ensemble weather forecasts are generated by perturbing the initial conditions of the forecast using a subset of the singular vectors of the linearised propagator. Previous results show that when creating probabilistic forecasts from this ensemble better forecasts are obtained if the mean of the spread and the variability of the spread are calibrated separately. We show results from a simple linear model that suggest that this may be a generic property for all singular vector based ensemble forecasting systems based on only a subset of the full set of singular vectors.

Autopoiesis vs. social autopoiesis: critical evaluation and implications for understanding firms as autopoietic social systems

The main objective of this study is to revisit the fundamental postulations of autopoietic self-production wrapped within the autopoietic six-point key and to investigate whether or not firms as specific social systems can be treated as autopoietic unities. In order to do so firms have to be defined as simple and composite unities whereupon their boundaries have to be clearly identifiable. The test of social autopoiesis reveals that firms can be viewed as autopoietic social systems that exist in the communicative space with employees' firm-specific communicative sub-domains as their components. Furthermore, it is argued that the social reification of autopoiesis (autokoinopoiesis) in firms is quintessentially interconnected with physical autopoiesis of their employees (autophysiopoiesis). Discontiguous focus on productivity as firms' obvious physical implication may thus be upgraded by a very social nature of ideactivity, firms' only real survival force.

Understanding biodiversity effects on prey in multi-enemy systems

Biodiversity-ecosystem functioning theory would predict that increasing natural enemy richness should enhance prey consumption rate due to functional complementarity of enemy species. However, several studies show that ecological interactions among natural enemies may result in complex effects of enemy diversity on prey consumption. Therefore, the challenge in understanding natural enemy diversity effects is to predict consumption rates of multiple enemies taking into account effects arising from patterns of prey use together with species interactions. Here, we show how complementary and redundant prey use patterns result in additive and saturating effects, respectively, and how ecological interactions such as phenotypic niche shifts, synergy and intraguild predation enlarge the range of outcomes to include null, synergistic and antagonistic effects. This study provides a simple theoretical framework that can be applied to experimental studies to infer the biological mechanisms underlying natural enemy diversity effects on prey.

Unravelling the rationale of 'overgrazing' and stocking rates in the beef production systems of Central Brazil using a bi-criteria compromise programming model

In Central Brazil, the long-term sustainability of beef cattle systems is under threat over vast tracts of farming areas, as more than half of the 50 million hectares of sown pastures are suffering from degradation. Overgrazing practised to maintain high stocking rates is regarded as one of the main causes. High stocking rates are deliberate and crucial decisions taken by the farmers, which appear paradoxical, even irrational given the state of knowledge regarding the consequences of overgrazing. The phenomenon however appears inextricably linked with the objectives that farmers hold. In this research those objectives were elicited first and from their ranking two, ‘asset value of cattle (representing cattle ownership)' and ‘present value of economic returns', were chosen to develop an original bi-criteria Compromise Programming model to test various hypotheses postulated to explain the overgrazing behaviour. As part of the model a pasture productivity index is derived to estimate the pasture recovery cost. Different scenarios based on farmers' attitudes towards overgrazing, pasture costs and capital availability were analysed. The results of the model runs show that benefits from holding more cattle can outweigh the increased pasture recovery and maintenance costs. This result undermines the hypothesis that farmers practise overgrazing because they are unaware or uncaring about overgrazing costs. An appropriate approach to the problem of pasture degradation requires information on the economics, and its interplay with farmers' objectives, for a wide range of pasture recovery and maintenance methods. Seen within the context of farmers' objectives, some level of overgrazing appears rational. Advocacy of the simple ‘no overgrazing' rule is an insufficient strategy to maintain the long-term sustainability of the beef production systems in Central Brazil.

Unravelling the rationale of 'overgrazing' and stocking rates in the beef production systems of Central Brazil using a bi-criteria compromise programming model

In Central Brazil, the long-term, sustainability of beef cattle systems is under threat over vast tracts of farming areas, as more than half of the 50 million hectares of sown pastures are suffering from. degradation. Overgrazing practised to maintain high stocking rates is regarded as one of the main causes. High stocking rates are deliberate and crucial decisions taken by the farmers, which appear paradoxical, even irrational given the state of knowledge regarding the consequences of overgrazing. The phenomenon however appears inextricably linked with the objectives that farmers hold. In this research those objectives were elicited first and from their ranking two, 'asset value of cattle (representing cattle ownership and 'present value of economic returns', were chosen to develop an original bi-criteria Compromise Programming model to test various hypotheses postulated to explain the overgrazing behaviour. As part of the model a pasture productivity index is derived to estimate the pasture recovery cost. Different scenarios based on farmers' attitudes towards overgrazing, pasture costs and capital availability were analysed. The results of the model runs show that benefits from holding more cattle can outweigh the increased pasture recovery and maintenance costs. This result undermines the hypothesis that farmers practise overgrazing because they are unaware or uncaring caring about overgrazing costs. An appropriate approach to the problem of pasture degradation requires information on the economics,and its interplay with farmers' objectives, for a wide range of pasture recovery and maintenance methods. Seen within the context of farmers' objectives, some level of overgrazing appears rational. Advocacy of the simple 'no overgrazing' rule is an insufficient strategy to maintain the long-term sustainability of the beef production systems in Central Brazil. (C) 2004 Elsevier Ltd. All rights reserved.

Evaluating the efficiency of sampling methods in assessing soil macrofauna communities in arable systems

The soil fauna is often a neglected group in many large-scale studies of farmland biodiversity due to difficulties in extracting organisms efficiently from the soil. This study assesses the relative efficiency of the simple and cheap sampling method of handsorting against Berlese-Tullgren funnel and Winkler apparatus extraction. Soil cores were taken from grassy arable field margins and wheat fields in Cambridgeshire, UK, and the efficiencies of the three methods in assessing the abundances and species densities of soil macroinver-tebrates were compared. Handsorting in most cases was as efficient at extracting the majority of the soil macrofauna as the Berlese-Tullgren funnel and Winkler bag methods, although it underestimated the species densities of the woodlice and adult beetles. There were no obvious biases among the three methods for the particular vegetation types sampled and no significant differences in the size distributions of the earthworms and beetles. Proportionally fewer damaged earthworms were recorded in larger (25 x 25 cm) soil cores when compared with smaller ones (15 x 15 cm). Handsorting has many benefits, including targeted extraction, minimum disturbance to the habitat and shorter sampling periods and may be the most appropriate method for studies of farmland biodiversity when a high number of soil cores need to be sampled. (C) 2008 Elsevier Masson SAS. All rights reserved.

Graphical tracking systems revisited: a practical approach to computer scheduling in horticulture

Graphical tracking is a technique for crop scheduling where the actual plant state is plotted against an ideal target curve which encapsulates all crop and environmental characteristics. Management decisions are made on the basis of the position of the actual crop against the ideal position. Due to the simplicity of the approach it is possible for graphical tracks to be developed on site without the requirement for controlled experimentation. Growth models and graphical tracks are discussed, and an implementation of the Richards curve for graphical tracking described. In many cases, the more intuitively desirable growth models perform sub-optimally due to problems with the specification of starting conditions, environmental factors outside the scope of the original model and the introduction of new cultivars. Accurate specification for a biological model requires detailed and usually costly study, and as such is not adaptable to a changing cultivar range and changing cultivation techniques. Fitting of a new graphical track for a new cultivar can be conducted on site and improved over subsequent seasons. Graphical tracking emphasises the current position relative to the objective, and as such does not require the time consuming or system specific input of an environmental history, although it does require detailed crop measurement. The approach is flexible and could be applied to a variety of specification metrics, with digital imaging providing a route for added value. For decision making regarding crop manipulation from the observed current state, there is a role for simple predictive modelling over the short term to indicate the short term consequences of crop manipulation.

Economic models and algorithms for distributed systems

Distributed computing paradigms for sharing resources such as Clouds, Grids, Peer-to-Peer systems, or voluntary computing are becoming increasingly popular. While there are some success stories such as PlanetLab, OneLab, BOINC, BitTorrent, and SETI@home, a widespread use of these technologies for business applications has not yet been achieved. In a business environment, mechanisms are needed to provide incentives to potential users for participating in such networks. These mechanisms may range from simple non-monetary access rights, monetary payments to specific policies for sharing. Although a few models for a framework have been discussed (in the general area of a "Grid Economy"), none of these models has yet been realised in practice. This book attempts to fill this gap by discussing the reasons for such limited take-up and exploring incentive mechanisms for resource sharing in distributed systems. The purpose of this book is to identify research challenges in successfully using and deploying resource sharing strategies in open-source and commercial distributed systems.

A simulation model of self-organising evolvability in software systems

The evolvability of a software artifact is its capacity for producing heritable or reusable variants; the inverse quality is the artifact's inertia or resistance to evolutionary change. Evolvability in software systems may arise from engineering and/or self-organising processes. We describe our 'Conditional Growth' simulation model of software evolution and show how, it can be used to investigate evolvability from a self-organisation perspective. The model is derived from the Bak-Sneppen family of 'self-organised criticality' simulations. It shows good qualitative agreement with Lehman's 'laws of software evolution' and reproduces phenomena that have been observed empirically. The model suggests interesting predictions about the dynamics of evolvability and implies that much of the observed variability in software evolution can be accounted for by comparatively simple self-organising processes.