Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

A competitive growth model with endogenous fertility

This paper investigates the interaction between endogenous fertility behavior and the distribution of income and wealth arnong farnilies in a competitive market economy. We construct a growth model in which altruistic dynasties are heterogeneous in their initial stocks of physical capital. Dynasties make choices of farnily size along with decisions about consumption and intergenerational transfers. We show that if the rate of time preference is increasing in the number of children and preferences over nurnber of children satisfy a norrnality assumption, all steady states are characterized by equality of capital stocks and consumption arnong families. We also provide sufficient conditions for uniqueness of the steady state. In order to illustrate these results, we present an example in which preferences over number of children are logarithrnic and the technology is Cobb-Douglas. For this combination of preferences and technology, there exists a unique egalitarian steady state. Moreover, the economy converges to this steady state in only one generation .

Optimal price regulation in a growth model with monopolistic suppliers of intermediate goods

In this paper we investigate the trade-off faced by regulators who must set a price for an intermediate good somewhere between the marginal cost and the monopoly price. We utilize a growth model with monopolistic suppliers of intermediate goods. Investment in innovation is required to produce a new intermediate good. Marginal cost pricing deters innovation, while monopoly pricing maximizes innovation and economic growth at the cost of some static inefficiency. We demonstrate the existence of a second-best price above the marginal cost but below the monopoly price, which maximizes consumer welfare. Simulation results suggest that substantial reductions in consumption, production, growth, and welfare occur where regulators focus on static efficiency issues by setting prices at or near marginal cost.

An improved Fabens method for estimation of growth parameters in the vonBertalanffy model with individual asymptotes

In the analysis of tagging data, it has been found that the least-squares method, based on the increment function known as the Fabens method, produces biased estimates because individual variability in growth is not allowed for. This paper modifies the Fabens method to account for individual variability in the length asymptote. Significance tests using t-statistics or log-likelihood ratio statistics may be applied to show the level of individual variability. Simulation results indicate that the modified method reduces the biases in the estimates to negligible proportions. Tagging data from tiger prawns (Penaeus esculentus and Penaeus semisulcatus) and rock lobster (Panulirus ornatus) are analysed as an illustration.

An environmentally based growth model that uses finite difference calculus with maximum likelihood method: its application to the brackish water bivalve Corbicula japonica in Lake Abashiri, Japan

We present a growth analysis model that combines large amounts of environmental data with limited amounts of biological data and apply it to Corbicula japonica. The model uses the maximum-likelihood method with the Akaike information criterion, which provides an objective criterion for model selection. An adequate distribution for describing a single cohort is selected from available probability density functions, which are expressed by location and scale parameters. Daily relative increase rates of the location parameter are expressed by a multivariate logistic function with environmental factors for each day and categorical variables indicating animal ages as independent variables. Daily relative increase rates of the scale parameter are expressed by an equation describing the relationship with the daily relative increase rate of the location parameter. Corbicula japonica grows to a modal shell length of 0.7 mm during the first year in Lake Abashiri. Compared with the attain-able maximum size of about 30 mm, the growth of juveniles is extremely slow because their growth is less susceptible to environmental factors until the second winter. The extremely slow growth in Lake Abashiri could be a geographical genetic variation within C. japonica.

Hysteresis and avalanches in the T=0 random field ising model with 2-spin flip dynamics

We study the nonequilibrium behavior of the three-dimensional Gaussian random-field Ising model at T=0 in the presence of a uniform external field using a two-spin-flip dynamics. The deterministic, history-dependent evolution of the system is compared with the one obtained with the standard one-spin-flip dynamics used in previous studies of the model. The change in the dynamics yields a significant suppression of coercivity, but the distribution of avalanches (in number and size) stays remarkably similar, except for the largest ones that are responsible for the jump in the saturation magnetization curve at low disorder in the thermodynamic limit. By performing a finite-size scaling study, we find strong evidence that the change in the dynamics does not modify the universality class of the disorder-induced phase transition.

Random-field Potts model with dipolarlike interactions: Hysteresis avalanches and microstructure

A model for the study of hysteresis and avalanches in a first-order phase transition from a single variant phase to a multivariant phase is presented. The model is based on a modification of the random-field Potts model with metastable dynamics by adding a dipolar interaction term truncated at nearest neighbors. We focus our study on hysteresis loop properties, on the three-dimensional microstructure formation, and on avalanche statistics.

Segmentation of brain tumor images based on atlas-registration combined with a Markov-Random-Field lesion growth model

We present an automatic method to segment brain tissues from volumetric MRI brain tumor images. The method is based on non-rigid registration of an average atlas in combination with a biomechanically justified tumor growth model to simulate soft-tissue deformations caused by the tumor mass-effect. The tumor growth model, which is formulated as a mesh-free Markov Random Field energy minimization problem, ensures correspondence between the atlas and the patient image, prior to the registration step. The method is non-parametric, simple and fast compared to other approaches while maintaining similar accuracy. It has been evaluated qualitatively and quantitatively with promising results on eight datasets comprising simulated images and real patient data.

The development and stability analysis of a nonlinear growth model for microorganisms

A nonlinear dynamic model of microbial growth is established based on the theories of the diffusion response of thermodynamics and the chemotactic response of biology. Except for the two traditional variables, i.e. the density of bacteria and the concentration of attractant, the pH value, a crucial influencing factor to the microbial growth, is also considered in this model. The pH effect on the microbial growth is taken as a Gaussian function G0e-(f- fc)2/G1, where G0, G1 and fc are constants, f represents the pH value and fc represents the critical pH value that best fits for microbial growth. To study the effects of the reproduction rate of the bacteria and the pH value on the stability of the system, three parameters a, G0 and G1 are studied in detail, where a denotes the reproduction rate of the bacteria, G0 denotes the impacting intensity of the pH value to microbial growth and G1 denotes the bacterial adaptability to the pH value. When the effect of the pH value of the solution which microorganisms live in is ignored in the governing equations of the model, the microbial system is more stable with larger a. When the effect of the bacterial chemotaxis is ignored, the microbial system is more stable with the larger G1 and more unstable with the larger G0 for f0 > fc. However, the stability of the microbial system is almost unaffected by the variation G0 and G1 and it is always stable for f0 < fc under the assumed conditions in this paper. In the whole system model, it is more unstable with larger G1 and more stable with larger G0 for f0 < fc. The system is more stable with larger G1 and more unstable with larger G0 for f0 > fc. However, the system is more unstable with larger a for f0 < fc and the stability of the system is almost unaffected by a for f0 > fc. The results obtained in this study provide a biophysical insight into the understanding of the growth and stability behavior of microorganisms.

Integrated sustainable urban infrastructure management: the Brisbane urban growth model

Sustainable urban development and the liveability of a city are increasingly important issues in the context of land use planning and infrastructure management. In recent years, the promotion of sustainable urban development in Australia and overseas is facing various physical, socio-economic and environmental challenges. These challenges and problems arise from the lack of capability of local governments to accommodate the needs of the population and economy in a relatively short timeframe. The planning of economic growth and development is often dealt with separately and not included in the conventional land use planning process. There is also a sharp rise in the responsibilities and roles of local government for infrastructure planning and management. This increase in responsibilities means that local elected officials and urban planners have less time to prepare background information and make decisions. The Brisbane Urban Growth Model has proven initially successful in providing a dynamic platform to ensure timely and coordinated delivery of urban infrastructure. Most importantly, this model is the first step for local governments in moving toward a systematic approach to pursuing sustainable and effective urban infrastructure management.

Integrated sustainable urban infrastructure management : the Brisbane urban growth model

Sustainable urban development and the liveability of a city are increasingly important issues in the context of land use planning and infrastructure management. In recent years, the promotion of sustainable urban development in Australia and overseas is facing various physical, socioeconomic and environmental challenges. These challenges and problems arise from the lack of capability of local governments to accommodate the needs of the population and economy in a relatively short timeframe. The planning of economic growth and development is often dealt with separately and not included in the conventional land use planning process. There is also a sharp rise in the responsibilities and roles of local government for infrastructure planning and management. This increase in responsibilities means that local elected officials and urban planners have less time to prepare background information and make decisions. The Brisbane Urban Growth Model has proven initially successful in providing a dynamic platform to ensure timely and coordinated delivery of urban infrastructure. Most importantly, this model is the first step for local governments in moving toward a systematic approach to pursuing sustainable and effective urban infrastructure management.

Accounting for individual variability in the von Bertalanffy growth model

Estimation of von Bertalanffy growth parameters has received considerable attention in fisheries research. Since Sainsbury (1980, Can. J. Fish. Aquat. Sci. 37: 241-247) much of this research effort has centered on accounting for individual variability in the growth parameters. In this paper we demonstrate that, in analysis of tagging data, Sainsbury's method and its derivatives do not, in general, satisfactorily account for individual variability in growth, leading to inconsistent parameter estimates (the bias does not tend to zero as sample size increases to infinity). The bias arises because these methods do not use appropriate conditional expectations as a basis for estimation. This bias is found to be similar to that of the Fabens method. Such methods would be appropriate only under the assumption that the individual growth parameters that generate the growth increment were independent of the growth parameters that generated the initial length. However, such an assumption would be unrealistic. The results are derived analytically, and illustrated with a simulation study. Until techniques that take full account of the appropriate conditioning have been developed, the effect of individual variability on growth has yet to be fully understood.

Growth curves with time-dependent explanatory variables

A class of growth models incorporating time-dependent factors and stochastic perturbations are introduced. The proposed model includes the existing growth models used in fisheries as special cases. Particular attention is given to growth of a population (in average weight or length) from which observations are taken randomly each time and the analysis of tag-recapture data. Two real data sets are used for illustration: (a) to estimate the seasonal effect and population density effect on growth of farmed prawn (Penaeus monodon) from weight data and (b) to assess the effect of tagging on growth of barramundi (Lates calcarifer)