Analysis of logistic growth models

A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most successful predictive models are shown to be based on extended forms of the classical Verhulst logistic growth equation. We further review and compare several such models and calculate and investigate properties of interest for these. We also identify and detail several previously unreported associated limitations and restrictions. A generalized form of the logistic growth curve is introduced which is shown incorporate these models as special cases. The reported limitations of the generic growth model are shown to be addressed by this new model and similarities between this and the extended growth curves are identified. Several of its properties are also presented. We furthermore show that additional growth characteristics are accommodated by this new model, enabling previously unsupported, untypical population dynamics to be modelled by judicious choice of model parameter values alone

Prediction of power generation from a wind farm

Wind farms produce a variable power output depending on the wind speed. For management of power networks and for bidding for the supply of power, the future power available needs to be predicted for time intervals ahead of a few minutes to about 24 hours. This project used data from a wind farm and three meteorological stations to determine methods and ability to predict wind speed. Analyses using regression, neural networks, and a Kalman filter were examined. Prediction using a combination of local wind measure-ments and meteorological data appears to give the best results

Analysis of reinforcement learning strategies for predation in a mimic-model prey environment

In this paper we propose a mathematical learning model for a stochastic automaton simulating the behaviour of a predator operating in a random environment occupied by two types of prey: palatable mimics and unpalatable models. Specifically, a well known linear reinforcement learning algorithm is used to update the probabilities of the two actions, eat prey or ignore prey, at every random encounter. Each action elicits a probabilistic response from the environment that can be either favorable or unfavourable. We analyse both fixed and varying stochastic responses for the system. The basic approach of mimicry is defined and a short review of relevant previous approaches in the literature is given. Finally, the conditions for continuous predator performance improvement are explicitly formulated and precise definitions of predatory efficiency and mimicry efficiency are also provided

Deterministic and stochastic optimal inventory control with logistic stock-dependent demand rate

It has been suggested by many supply chain practitioners that in certain cases inventory can have a stimulating effect on the demand. In mathematical terms this amounts to the demand being a function of the inventory level alone. In this work we propose a logistic growth model for the inventory dependent demand rate and solve first the continuous time deterministic optimal control problem of maximising the present value of the total net profit over an infinite horizon. It is shown that under a strict condition there is a unique optimal stock level which the inventory planner should maintain in order to satisfy demand. The stochastic version of the optimal control problem is considered next. A bang-bang type of optimal control problem is formulated and the associated Hamilton-Jacobi-Bellman equation is solved. The inventory level that signifies a switch in the ordering strategy is worked out in the stochastic case. Copyright © 2014 Inderscience Enterprises Ltd

An optimal inventory pricing and ordering strategy subject to demand dependent on stock level and price

This article considers the deterministic singular optimal control problem of profit maximisation for inventory replenished at a variable rate and depleted by demand which is assumed to vary with price and stock availability. Optimal policies for the product order rate and price are derived using the maximum principle. Several initial inventory regions are identified as potential inventory states for feasible profit optimisation. Bounds on the maximum price for maximising net profit or minimising loss are obtained. Numerical simulations accompanied by phase diagrams are performed to support the theoretical findings

On Some Important Ordinary Differential Equations of Dynamic Economics

Mathematical modeling in economics became central to economic theory during the decade of the Second World War. The leading figure in that period was Paul Anthony Samuelson whose 1947 book, Foundations of Economic Analysis, formalized the problem of dynamic analysis in economics. In this brief chapter some seminal applications of differential equations in economic growth, capital and business trade cycles are outlined in deterministic setting. Chaos and bifurcations in economic dynamics are not considered. Explicit analytical solutions are presented only in relatively straightforward cases and in more complicated cases a path to the solution is outlined. Differential equations in modern dynamic economic modeling are extensions and modifications of these classical works. Finally we would like to stress that the differential equations presented in this chapter are of the “stand-alone” type in that they were solely introduced to model economic growth and trade cycles. Partial differential equations such as those which arise in related fields, like Bioeconomics and Differential Games, from optimizing the Hamiltonian of the problem, and stochastic differential equations of Finance and Macroeconomics are not considered here

An Optimal Inventory Pricing and Ordering Strategy Subject to Stock and Price Dependent Demand

This article considers the deterministic optimal control problem of profit maximization for inventory replenished at a variable rate and depleted by demand which is assumed to vary with price and stock availability. Optimal policies for the inventor, product order rate and price are derived using the maximum principle. Bounds on the maximum price possible are also derived

Identification of Crisis Management Influencing Factors in the Abu Dhabi Police Force, United Arab Emirates

Through various disasters, due to both anthropological and natural causes, the development of effective crisis management (CM) mechanisms has become inevitably critical in order to reduce not only various types of losses, but also the potential magnitude of future calamities (Sahin, 2009). Although a number of researchers examined effective CM in organisations located in and/or managed by Western countries (Adams and Stewart, 2014), little has been conducted in the United Arab Emirates (UAE). In fact, to date, there has been no such research applied to any UAE police department. Thus, this study aims to review CM within the General Headquarters (GHQ) of Abu Dhabi Police in order to identify potential influencing factors contributing to effective CM in the organisation, and eventually develop a holistic framework based on global benchmarking

Spatio-temporal stochastic resonance induces patterns in wetland vegetation dynamics

Water availability is a major environmental driver affecting riparian and wetland vegetation. The interaction between water table fluctuations and vegetation in a stochastic environment contributes to the complexity of the dynamics of these ecosystems. We investigate the possible emergence of spatial patterns induced by spatio-temporal stochastic resonance in a simple model of groundwater-dependent ecosystems. These spatio-temporal dynamics are driven by the combined effect of three components: (i) an additive white Gaussian noise, accounting for external random disturbances such as fires or fluctuations in rain water availability, (ii) a weak periodic modulation in time, describing hydrological drivers such as seasonal fluctuations of water table depth, and (iii) a spatial coupling term, which takes into account the ability of vegetation to spread and colonize other parts of the landscape. A suitable cooperation between these three terms is able to give rise to ordered structures which show spatial and temporal coherence, and are statistically steady in time.Comment: 9 pages, 7 figure

Effect of bacterial nanocellulose binding on the bactericidal activity of bovine lactoferrin

Bovine lactoferrin (bLF) has been extensively described as a wide spectrum antimicrobial protein. bLF bactericidal activity has been mainly attributed to two different mechanisms: environmental iron depletion and cell membrane destabilization. Due to its antimicrobial properties, bLF has been included in the formulation nutraceutical food products and edible active packages. This work comprises the experimental evidence of the requirement of bLF unrestricted mobility (free bLF) to effectively perform its bactericidal action. To assess the unrestricted and restricted bLF activity, a nontoxic matrix of bacterial nanocellulose (BNC) was used as carrier, and as an anchoring scaffold, respectively. Therefore, BNC was functionalized with bLF through two different methodologies: (i) bLF was embedded within the three-dimensional structure of BNC and; (ii) bLF was covalently bounded to the nanofibrils of BNC. bLF efficiency was tested against two bacteria isolated from clinical specimens, Escherichia coli and Staphylococcus aureus. bLF concentration after covalent binding to BNC was two-fold higher in comparison to the embedding method. Nevertheless, only the embedded bLF exhibited a significant bactericidal activity, due to bLF ability to permeate the BNC matrix and execute its bactericidal action.Portuguese Foundation for Science and Technology (FCT) under the scope of the strategic funding of UIDB/ 04469/2020 unit and BioTecNorte operation (NORTE-01-0145-FEDER- 000004) funded by the European Regional Development Fund under the scope of Norte2020 - Programa Operacional Regional do NortePortuguese Foundation for Science and Technology (FCT) in the framework of the Strategic Funding of UID/FIS/04650/2020 and projects PTDC/BTM-MAT/28237/ 2017 and PTDC/EMDEMD/28159/2017Portuguese Foundation for Science and Technology (FCT) SFRH/BD/64901/2009 and SFRH/BD/111478/2015Spanish State Research Agency (AEI) and the European Regional Development Fund through the project PID2019-106099RBC43/ AEI/10.13039/501100011033 and from the Basque Government Industry and Education Department under the ELKARTEK, HAZITEK and PIBA (PIBA-2018-06) programs, respectivelyinfo:eu-repo/semantics/publishedVersio