Onset And Characterisation Of Chaos In A Two Dimensional Nonlinear Deterministic Model

Nature is full of phenomena which we call "chaotic", the weather being a prime example. What we mean by this is that we cannot predict it to any significant accuracy, either because the system is inherently complex, or because some of the governing factors are not deterministic. However, during recent years it has become clear that random behaviour can occur even in very simple systems with very few number of degrees of freedom, without any need for complexity or indeterminacy. The discovery that chaos can be generated even with the help of systems having completely deterministic rules - often models of natural phenomena - has stimulated a lo; of research interest recently. Not that this chaos has no underlying order, but it is of a subtle kind, that has taken a great deal of ingenuity to unravel. In the present thesis, the author introduce a new nonlinear model, a ‘modulated’ logistic map, and analyse it from the view point of ‘deterministic chaos‘.

A deterministic model for lake clarity; application to management of Lake Tahoe (California-Nevada), USA

This dissertation has as its goal the quantitative evaluation of the application of coupled hydrodynamic, ecological and clarity models, to address the deterministic prediction of water clarity in lakes and reservoirs. Prediction of water clarity is somewhat unique, insofar as it represents the integrated and coupled effects of a broad range of individual water quality components. These include the biological components such as phytoplankton, together with the associated cycles of nutrients that are needed to sustain their popuiations, and abiotic components such as suspended particles that may be introduced by streams, atmospheric deposition or sediment resuspension. Changes in clarity induced by either component will feed back on the phytoplankton dynamics, as incident light also affects biological growth. Thus ability to successfully model changes in clarity will by necessity have to achieve the correct modeling of these other water quality parameters. Water clarity is also unique in that it may be one of the earliest and most easily detected wamings of the acceleration of the process of eutrophication in a water body.

Stochastic model for simulating maize yield

Maize is one of the most important crops in the world. The products generated from this crop are largely used in the starch industry, the animal and human nutrition sector, and biomass energy production and refineries. For these reasons, there is much interest in figuring the potential grain yield of maize genotypes in relation to the environment in which they will be grown, as the productivity directly affects agribusiness or farm profitability. Questions like these can be investigated with ecophysiological crop models, which can be organized according to different philosophies and structures. The main objective of this work is to conceptualize a stochastic model for predicting maize grain yield and productivity under different conditions of water supply while considering the uncertainties of daily climate data. Therefore, one focus is to explain the model construction in detail, and the other is to present some results in light of the philosophy adopted. A deterministic model was built as the basis for the stochastic model. The former performed well in terms of the curve shape of the above-ground dry matter over time as well as the grain yield under full and moderate water deficit conditions. Through the use of a triangular distribution for the harvest index and a bivariate normal distribution of the averaged daily solar radiation and air temperature, the stochastic model satisfactorily simulated grain productivity, i.e., it was found that 10,604 kg ha(-1) is the most likely grain productivity, very similar to the productivity simulated by the deterministic model and for the real conditions based on a field experiment. © 2012 American Society of Agricultural and Biological Engineers.

Comparison of deterministic, stochastic and fuzzy logic uncertainty modelling for capacity extension projects of DI/WFI pharmaceutical plant utilities with variable/dynamic demand

The last 30 years have seen Fuzzy Logic (FL) emerging as a method either complementing or challenging stochastic methods as the traditional method of modelling uncertainty. But the circumstances under which FL or stochastic methods should be used are shrouded in disagreement, because the areas of application of statistical and FL methods are overlapping with differences in opinion as to when which method should be used. Lacking are practically relevant case studies comparing these two methods. This work compares stochastic and FL methods for the assessment of spare capacity on the example of pharmaceutical high purity water (HPW) utility systems. The goal of this study was to find the most appropriate method modelling uncertainty in industrial scale HPW systems. The results provide evidence which suggests that stochastic methods are superior to the methods of FL in simulating uncertainty in chemical plant utilities including HPW systems in typical cases whereby extreme events, for example peaks in demand, or day-to-day variation rather than average values are of interest. The average production output or other statistical measures may, for instance, be of interest in the assessment of workshops. Furthermore the results indicate that the stochastic model should be used only if found necessary by a deterministic simulation. Consequently, this thesis concludes that either deterministic or stochastic methods should be used to simulate uncertainty in chemical plant utility systems and by extension some process system because extreme events or the modelling of day-to-day variation are important in capacity extension projects. Other reasons supporting the suggestion that stochastic HPW models are preferred to FL HPW models include: 1. The computer code for stochastic models is typically less complex than a FL models, thus reducing code maintenance and validation issues. 2. In many respects FL models are similar to deterministic models. Thus the need for a FL model over a deterministic model is questionable in the case of industrial scale HPW systems as presented here (as well as other similar systems) since the latter requires simpler models. 3. A FL model may be difficult to "sell" to an end-user as its results represent "approximate reasoning" a definition of which is, however, lacking. 4. Stochastic models may be applied with some relatively minor modifications on other systems, whereas FL models may not. For instance, the stochastic HPW system could be used to model municipal drinking water systems, whereas the FL HPW model should or could not be used on such systems. This is because the FL and stochastic model philosophies of a HPW system are fundamentally different. The stochastic model sees schedule and volume uncertainties as random phenomena described by statistical distributions based on either estimated or historical data. The FL model, on the other hand, simulates schedule uncertainties based on estimated operator behaviour e.g. tiredness of the operators and their working schedule. But in a municipal drinking water distribution system the notion of "operator" breaks down. 5. Stochastic methods can account for uncertainties that are difficult to model with FL. The FL HPW system model does not account for dispensed volume uncertainty, as there appears to be no reasonable method to account for it with FL whereas the stochastic model includes volume uncertainty.

Remanufacturer-Manufacturer Collaborative Model in the Smae Channel

This paper adds to the growing literature of market competition related to the remanufacturer by analyzing the model where the remanufacturer and the manufacturer collaborate with each other in the same channel. This paper investigates a single-period deterministic model which keeps the analysis simple so as to obtain sharper insights. The results characterize the optimal remanufacturing and pricing strategies for the remanufacturer and the manufacturer in the collaborative model

STOCHASTIC MODEL FOR SIMULATING MAIZE YIELD

Maize is one of the most important crops in the world. The products generated from this crop are largely used in the starch industry, the animal and human nutrition sector, and biomass energy production and refineries. For these reasons, there is much interest in figuring the potential grain yield of maize genotypes in relation to the environment in which they will be grown, as the productivity directly affects agribusiness or farm profitability. Questions like these can be investigated with ecophysiological crop models, which can be organized according to different philosophies and structures. The main objective of this work is to conceptualize a stochastic model for predicting maize grain yield and productivity under different conditions of water supply while considering the uncertainties of daily climate data. Therefore, one focus is to explain the model construction in detail, and the other is to present some results in light of the philosophy adopted. A deterministic model was built as the basis for the stochastic model. The former performed well in terms of the curve shape of the above-ground dry matter over time as well as the grain yield under full and moderate water deficit conditions. Through the use of a triangular distribution for the harvest index and a bivariate normal distribution of the averaged daily solar radiation and air temperature, the stochastic model satisfactorily simulated grain productivity, i.e., it was found that 10,604 kg ha(-1) is the most likely grain productivity, very similar to the productivity simulated by the deterministic model and for the real conditions based on a field experiment.

Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model

Generalised epileptic seizures are frequently accompanied by sudden, reversible transitions from low amplitude, irregular background activity to high amplitude, regular spike-wave discharges (SWD) in the EEG. The underlying mechanisms responsible for SWD generation and for the apparently spontaneous transitions to SWD and back again are still not fully understood. Specifically, the role of spatial cortico-cortical interactions in ictogenesis is not well studied. We present a macroscopic, neural mass model of a cortical column which includes two distinct time scales of inhibition. This model can produce both an oscillatory background and a pathological SWD rhythm. We demonstrate that coupling two of these cortical columns can lead to a bistability between out-of-phase, low amplitude background dynamics and in-phase, high amplitude SWD activity. Stimuli can cause state-dependent transitions from background into SWD. In an extended local area of cortex, spatial heterogeneities in a model parameter can lead to spontaneous reversible transitions from a desynchronised background to synchronous SWD due to intermittency. The deterministic model is therefore capable of producing absence seizure-like events without any time dependent adjustment of model parameters. The emergence of such mechanisms due to spatial coupling demonstrates the importance of spatial interactions in modelling ictal dynamics, and in the study of ictogenesis.

Development of an adequate model for verification of design safety-margins of the HTTR nuclear test facility

This work is based on the prototype High Engineering Test Reactor (HTTR) of the Japan Agency of Energy Atomic (JAEA). Its objective is to describe an adequate deterministic model to be used in the assessment of its design safety margins via damage domains. The concept of damage domain is defined and it is shown its relevance in the ongoing effort to apply dynamic risk assessment methods and tools based on the Theory of Stimulated Dynamics (TSD). To illustrate, we present results of an abnormal control rod (CR) withdrawal during subcritical condition and its comparison with results obtained by JAEA. No attempt is made yet to actually assess the detailed scenarios, rather to show how the approach may handle events of its kind

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.

Parameter Identification in a Tuberculosis Model for Cameroon

A deterministic model of tuberculosis in Cameroon is designed and analyzed with respect to its transmission dynamics. The model includes lack of access to treatment and weak diagnosis capacity as well as both frequency-and density-dependent transmissions. It is shown that the model is mathematically well-posed and epidemiologically reasonable. Solutions are non-negative and bounded whenever the initial values are non-negative. A sensitivity analysis of model parameters is performed and the most sensitive ones are identified by means of a state-of-the-art Gauss-Newton method. In particular, parameters representing the proportion of individuals having access to medical facilities are seen to have a large impact on the dynamics of the disease. The model predicts that a gradual increase of these parameters could significantly reduce the disease burden on the population within the next 15 years.

Towards a predictive model of Ca²⁺ puffs

We investigate key characteristics of Ca²⁺ puffs in deterministic and stochastic frameworks that all incorporate the cellular morphology of IP[subscript]3 receptor channel clusters. In a first step, we numerically study Ca²⁺ liberation in a three dimensional representation of a cluster environment with reaction-diffusion dynamics in both the cytosol and the lumen. These simulations reveal that Ca²⁺ concentrations at a releasing cluster range from 80 µM to 170 µM and equilibrate almost instantaneously on the time scale of the release duration. These highly elevated Ca²⁺ concentrations eliminate Ca²⁺ oscillations in a deterministic model of an IP[subscript]3R channel cluster at physiological parameter values as revealed by a linear stability analysis. The reason lies in the saturation of all feedback processes in the IP[subscript]3R gating dynamics, so that only fluctuations can restore experimentally observed Ca²⁺ oscillations. In this spirit, we derive master equations that allow us to analytically quantify the onset of Ca²⁺ puffs and hence the stochastic time scale of intracellular Ca²⁺ dynamics. Moving up the spatial scale, we suggest to formulate cellular dynamics in terms of waiting time distribution functions. This approach prevents the state space explosion that is typical for the description of cellular dynamics based on channel states and still contains information on molecular fluctuations. We illustrate this method by studying global Ca²⁺ oscillations.

Effect of pedestrian movement on MIMO-OFDM channel capacity in an indoor environment

The rapid growth of mobile telephone use, satellite services, and now the wireless Internet and WLANs are generating tremendous changes in telecommunication and networking. As indoor wireless communications become more prevalent, modeling indoor radio wave propagation in populated environments is a topic of significant interest. Wireless MIMO communication exploits phenomena such as multipath propagation to increase data throughput and range, or reduce bit error rates, rather than attempting to eliminate effects of multipath propagation as traditional SISO communication systems seek to do. The MIMO approach can yield significant gains for both link and network capacities, with no additional transmitting power or bandwidth consumption when compared to conventional single-array diversity methods. When MIMO and OFDM systems are combined and deployed in a suitable rich scattering environment such as indoors, a significant capacity gain can be observed due to the assurance of multipath propagation. Channel variations can occur as a result of movement of personnel, industrial machinery, vehicles and other equipment moving within the indoor environment. The time-varying effects on the propagation channel in populated indoor environments depend on the different pedestrian traffic conditions and the particular type of environment considered. A systematic measurement campaign to study pedestrian movement effects in indoor MIMO-OFDM channels has not yet been fully undertaken. Measuring channel variations caused by the relative positioning of pedestrians is essential in the study of indoor MIMO-OFDM broadband wireless networks. Theoretically, due to high multipath scattering, an increase in MIMO-OFDM channel capacity is expected when pedestrians are present. However, measurements indicate that some reductions in channel capacity could be observed as the number of pedestrians approaches 10 due to a reduction in multipath conditions as more human bodies absorb the wireless signals. This dissertation presents a systematic characterization of the effects of pedestrians in indoor MIMO-OFDM channels. Measurement results, using the MIMO-OFDM channel sounder developed at the CSIRO ICT Centre, have been validated by a customized Geometric Optics-based ray tracing simulation. Based on measured and simulated MIMO-OFDM channel capacity and MIMO-OFDM capacity dynamic range, an improved deterministic model for MIMO-OFDM channels in indoor populated environments is presented. The model can be used for the design and analysis of future WLAN to be deployed in indoor environments. The results obtained show that, in both Fixed SNR and Fixed Tx for deterministic condition, the channel capacity dynamic range rose with the number of pedestrians as well as with the number of antenna combinations. In random scenarios with 10 pedestrians, an increment in channel capacity of up to 0.89 bits/sec/Hz in Fixed SNR and up to 1.52 bits/sec/Hz in Fixed Tx has been recorded compared to the one pedestrian scenario. In addition, from the results a maximum increase in average channel capacity of 49% has been measured while 4 antenna elements are used, compared with 2 antenna elements. The highest measured average capacity, 11.75 bits/sec/Hz, corresponds to the 4x4 array with 10 pedestrians moving randomly. Moreover, Additionally, the spread between the highest and lowest value of the the dynamic range is larger for Fixed Tx, predicted 5.5 bits/sec/Hz and measured 1.5 bits/sec/Hz, in comparison with Fixed SNR criteria, predicted 1.5 bits/sec/Hz and measured 0.7 bits/sec/Hz. This has been confirmed by both measurements and simulations ranging from 1 to 5, 7 and 10 pedestrians.

Multivariate Markov Process Models for the transmission of methicillin-resistant Staphylococcus Aureus in a hospital ward

Methicillin-resistant Staphylococcus Aureus (MRSA) is a pathogen that continues to be of major concern in hospitals. We develop models and computational schemes based on observed weekly incidence data to estimate MRSA transmission parameters. We extend the deterministic model of McBryde, Pettitt, and McElwain (2007, Journal of Theoretical Biology 245, 470–481) involving an underlying population of MRSA colonized patients and health-care workers that describes, among other processes, transmission between uncolonized patients and colonized health-care workers and vice versa. We develop new bivariate and trivariate Markov models to include incidence so that estimated transmission rates can be based directly on new colonizations rather than indirectly on prevalence. Imperfect sensitivity of pathogen detection is modeled using a hidden Markov process. The advantages of our approach include (i) a discrete valued assumption for the number of colonized health-care workers, (ii) two transmission parameters can be incorporated into the likelihood, (iii) the likelihood depends on the number of new cases to improve precision of inference, (iv) individual patient records are not required, and (v) the possibility of imperfect detection of colonization is incorporated. We compare our approach with that used by McBryde et al. (2007) based on an approximation that eliminates the health-care workers from the model, uses Markov chain Monte Carlo and individual patient data. We apply these models to MRSA colonization data collected in a small intensive care unit at the Princess Alexandra Hospital, Brisbane, Australia.

Measurement, modelling and capacity analysis for novel, fixed multi-user single-antenna MIMO-OFDM system, in rural environments

High-speed broadband internet access is widely recognised as a catalyst to social and economic development. However, the provision of broadband Internet services with the existing solutions to rural population, scattered over an extensive geographical area, remains both an economic and technical challenge. As a feasible solution, the Commonwealth Scientific and Industrial Research Organization (CSIRO) proposed a highly spectrally efficient, innovative and cost-effective fixed wireless broadband access technology, which uses analogue TV frequency spectrum and Multi-User MIMO (MUMIMO) technology with Orthogonal-Frequency-Division-Multiplexing (OFDM). MIMO systems have emerged as a promising solution for the increasing demand of higher data rates, better quality of service, and higher network capacity. However, the performance of MIMO systems can be significantly affected by different types of propagation environments e.g., indoor, outdoor urban, or outdoor rural and operating frequencies. For instance, large spectral efficiencies associated with MIMO systems, which assume a rich scattering environment in urban environments, may not be valid for all propagation environments, such as outdoor rural environments, due to the presence of less scatterer densities. Since this is the first time a MU-MIMO-OFDM fixed broadband wireless access solution is deployed in a rural environment, questions from both theoretical and practical standpoints arise; For example, what capacity gains are available for the proposed solution under realistic rural propagation conditions?. Currently, no comprehensive channel measurement and capacity analysis results are available for MU-MIMO-OFDM fixed broadband wireless access systems which employ large scale multiple antennas at the Access Point (AP) and analogue TV frequency spectrum in rural environments. Moreover, according to the literature, no deterministic MU-MIMO channel models exist that define rural wireless channels by accounting for terrain effects. This thesis fills the aforementioned knowledge gaps with channel measurements, channel modeling and comprehensive capacity analysis for MU-MIMO-OFDM fixed wireless broadband access systems in rural environments. For the first time, channel measurements were conducted in a rural farmland near Smithton, Tasmania using CSIRO's broadband wireless access solution. A novel deterministic MU-MIMO-OFDM channel model, which can be used for accurate performance prediction of rural MUMIMO channels with dominant Line-of-Sight (LoS) paths, was developed under this research. Results show that the proposed solution can achieve 43.7 bits/s/Hz at a Signal-to- Noise Ratio (SNR) of 20 dB in rural environments. Based on channel measurement results, this thesis verifies that the deterministic channel model accurately predicts channel capacity in rural environments with a Root Mean Square (RMS) error of 0.18 bits/s/Hz. Moreover, this study presents a comprehensive capacity analysis of rural MU-MIMOOFDM channels using experimental, simulated and theoretical models. Based on the validated deterministic model, further investigations on channel capacity and the eects of capacity variation, with different user distribution angles (θ) around the AP, were analysed. For instance, when SNR = 20dB, the capacity increases from 15.5 bits/s/Hz to 43.7 bits/s/Hz as θ increases from 10° to 360°. Strategies to mitigate these capacity degradation effects are also presented by employing a suitable user grouping method. Outcomes of this thesis have already been used by CSIRO scientists to determine optimum user distribution angles around the AP, and are of great significance for researchers and MU-MUMO-OFDM system developers to understand the advantages and potential capacity gains of MU-MIMO systems in rural environments. Also, results of this study are useful to further improve the performance of MU-MIMO-OFDM systems in rural environments. Ultimately, this knowledge contribution will be useful in delivering efficient, cost-effective high-speed wireless broadband systems that are tailor-made for rural environments, thus, improving the quality of life and economic prosperity of rural populations.