Research Publications (Systems Science)

Permanent URI for this collectionhttp://ir-dev.dut.ac.za/handle/10321/842

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Consumption threshold used to investigate stability and ecological dominance in consumer-resource dynamics
(Elsevier, 2015) Collins, Obiora Cornelius; Duffy, Kevin Jan
Understanding consumer resource population dynamics can be important to an understanding of the overall ecology of systems. For example, the tree-grass continuum dynamics of savannas, an important ecological biome, is inﬂuenced by the population dynamics. Here we investigate herbivory driven popu-lation dynamics of a savanna using a simple model of the interactions of the dominant players, namely: trees, grasses, browsers, grazers and mixed browsers-grazers. We introduce a consumption threshold that summarises some of the parameters and this is used as a guide to understanding the dynamics. This number is used in investigating system stability and sensitivity to parameter ﬂuctuations. It is also used to identify degrees of ecological dominance.
Identifying stability conditions and Hopf bifurcations in a consumer resource model using a consumption threshold
(Elsevier, 2016) Duffy, Kevin Jan; Collins, Obiora Cornelius
The existence, or not, of cyclic dynamics is one of the pivotal aspects of ecological populations. This work considers a consumer resource model found in ecology that can describe both cyclic and non-cyclic dynamics depending on parameter conditions. A threshold consumption number C0 is introduced, similar to the basic reproduction in epidemiological models. It is shown that consumer survival requires C0 > 1 and that a Hopf bifurcation occurs at , where is defined here and is greater than 1. This result is discussed with an example and extensions to other more complicated models.
Microbiological water quality along Vaal Gamagara’s potable water distribution system
(Business Perspectives, 2015) Mokhosi, Agnes; Dzwairo, Bloodless
Safe drinking water is essential to all life forms. Thus analysis for microbiological parameters is critical as this assists in declaring the fitness of potable water for human consumption, among other sustainable and “green uses”. The aim of this paper is to investigate the microbiological quality of potable water along Vaal Gamagara Water Treatment Plant’s (VGWTP) distribution system. A total of 10 samples were collected weekly along the system. The samples were col-lected from January to December 2013 in order to analyze for Escherichia coli (E.coli), total coliforms (TC) and Hete-rotrophic plate counts (HPC). The results showed that only 0.1% and 0.4% of samples analyzed were positive for E. coli and total coliforms, respectively. However, HPC results showed that 40% of the samples analyzed from June to December 2013 had higher counts than the recommended standard limit. The chlorine residual showed an increase from June to December 2013. An assessment of the results indicated that the integrity of the system was compromised for the research period. Water quality failures in a distribution system are unacceptable because they threaten human health and sometimes result in loss of life. Thus the assessment called for an urgent need to boost chlorine residual especially at points further away from the treatment plant. This was envisaged to provide a safety net for microbial compliance while the system was critically and continuously monitored, and further investigations were performed. Studies on chlorine decay were recommended as a priority in order to optimize disinfection and maintain good quality drinking water throughout the system.
Understanding multiple species ecosystem dynamics using a consumer resource model
(Wiley, 2016) Collins, Obiora Cornelius; Duffy, Kevin Jan
Most ecological systems comprise multiple species coex-isting and the dynamics of these multiple species can be important for understanding, management, and conservation. One method to study such ecological system dynamics is the use of heterogeneous models. Here we for-mulate and analyze a multiple species (n patches or groups) consumer re-source model. Initial insights are gained by analyzing the special cases n =1 and n = 2. A threshold consumption number C0 is used to investigate system stability and hence the long-term dynamics of the system. It is shown how this threshold consumption number can measure the eﬀects and extent of multiple species coexistence in the system.