Research Publications (Systems Science)
Permanent URI for this collectionhttp://ir-dev.dut.ac.za/handle/10321/842
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Item Algorithm for solutions of nonlinear equations of strongly monotone type and applications to convex minimization and variational inequality problems(Hindawi Limited, 2020-08-01) Aibinu, Mathew O.; Thakur, Surendra C.; Moyo, SibusisoReal-life problems are governed by equations which are nonlinear in nature. Nonlinear equations occur in modeling problems, such as minimizing costs in industries and minimizing risks in businesses. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear is used to obtain a strong convergence result for nonlinear equations of (p, {\eta})-strongly monotone type, where {\eta} > 0, p > 1. An example is presented for the nonlinear equations of (p, {\eta})-strongly monotone type. As a consequence of the main result, the solutions of convex minimization and variational inequality problems are obtained. This solution has applications in other fields such as engineering, physics, biology, chemistry, economics, and game theory.Item Indigenous strategies and empirical models for adaptability of the maize-bean intercropping system to climate change(UZ Foundatoin, 2016-12) Mapanda, S.; Chitja, J. M.; Duffy, Kevin JanThis review article discusses on different ways of indigenous strategies and empirical models as an adaptation to climate change by smallholder farmers in Africa. Indigenous adaptation strategies are methods that enable individuals or communities to adjust to the impacts of climate change in local areas. Some of the strategies practiced are: zero tillage, mulching, soil management techniques, organic agriculture and fallow system of cultiva-tion, intercropping with legumes, early planting and use of tolerant varieties to drought, water conservation and crop diversification. Scientists developed many empirical models that are used to project the impact of climate change to agriculture. Some of the empirical models include: CERES-Maize Crop Model, Global Circulation Models (GCM) and histori-cal data records. There is also use of empirical evidence such as indigenous land unit framework, indigenous early warning systems, use of rainmakers, movement of birds, ants and crying of dogs by the indigenous smallholder farmers in Africa. Intercropping system is the best practice used as a strategy to climate change adaptability, and one of the most suitable intercropping systems is that of maize and bean. However, the current research findings revealed that there is a lack of consideration of indigenous knowledge that could enhance livelihoods that depend on natural resources directly affected by climate change.Item Symmetrized exponential oscillator(World Scientific Publishing, 2016-09-01) Znojil, MiloslavSeveral properties of bound states in potential V(x) = g² exp(Formula presented.)x(Formula presented.) are studied. Firstly, with the emphasis on the reliability of our arbitrary-precision construction, wave functions are considered in the two alternative (viz. asymptotically decreasing or regular) exact Bessel-function forms which obey the asymptotic or matching conditions, respectively. The merits of the resulting complementary transcendental secular equation approaches are compared and their applicability is discussed.Item Linear Quantum Entropy and Non-Hermitian Hamiltonians(MDPI, 2016-12-16) Sergi, Alessandro; Giaquinta, Paolo V.We consider the description of open quantum systems with probability sinks (or sources) in terms of general non-Hermitian Hamiltonians. Within such a framework, we study novel possible definitions of the quantum linear entropy as an indicator of the flow of information during the dynamics. Such linear entropy functionals are necessary in the case of a partially Wigner-transformed non-Hermitian Hamiltonian (which is typically useful within a mixed quantum-classical representation). Both the case of a system represented by a pure non-Hermitian Hamiltonian as well as that of the case of non-Hermitian dynamics in a classical bath are explicitly consideredItem Understanding multiple species ecosystem dynamics using a consumer resource model(Wiley, 2016) Collins, Obiora Cornelius; Duffy, Kevin JanMost 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.Item Consumption threshold used to investigate stability and ecological dominance in consumer-resource dynamics(Elsevier, 2015) Collins, Obiora Cornelius; Duffy, Kevin JanUnderstanding 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.Item Optimal control of maize foliar diseases using the plants population dynamics(Taylor and Fancis, 2015-09-28) Collins, Obiora Cornelius; Duffy, Kevin JanPathogens and insects can have important negative effects on yields of crops cultivated by humans. These effects can be important for the food security or financial well-being of individuals. In particular, maize is a very important staple crop worldwide and is vulnerable to diseases. We formulate here a mathematical model to evaluate the impacts of foliar diseases on the population dynamics of maize plants. Qualitative analyses of the important mathematical features of the model are carried out. We show how this methodology can be extended to reducing the spread of foliar diseases through effective control measures with minimum costs.Item Identifying stability conditions and Hopf bifurcations in a consumer resource model using a consumption threshold(Elsevier, 2016) Duffy, Kevin Jan; Collins, Obiora CorneliusThe 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.Item Quantum-statistical approach to electromagnetic wave propagation and dissipation inside dielectric media and nanophotonic and plasmonic waveguides(American Physical Society, 2016) Zloshchastiev, Konstantin G.Quantum-statistical effects occur during the propagation of electromagnetic (EM) waves inside the dielectric media or metamaterials, which include a large class of nanophotonic and plasmonic waveguides with dissipation and noise. Exploiting the formal analogy between the Schr¨odinger equation and the Maxwell equations for dielectric linear media, we rigorously derive the effective Hamiltonian operatorwhich describes such propagation. This operator turns out to be essentially non-Hermitian in general, and pseudo-Hermitian in some special cases. Using the density operator approach for general non-Hermitian Hamiltonians, we derive a master equation that describes the statistical ensembles of EM wave modes. The method also describes the quantum dissipative and decoherence processes which happen during the wave’s propagation, and, among other things, it reveals the conditions that are necessary to control the energy and information loss inside the above-mentioned materials.Item Non-Hermitian Hamiltonian Approach for Electromagnetic Wave Propagation and Dissipation tn Dielectric Media(IEEE, 2016-06) Zloshchastiev, Konstantin G.Using the formal analogy between a certain class of Maxwell equations and the Schrdinger equation, we derive the effective Hamiltonian operator that governs the propagation of electromagnetic (EM) wave modes inside nonconducting linear media, which include a large range of nanophotonic and plasmonic waveguides. It turns out that this Hamiltonian is essentially non-Hermitian, and thus requires a special treatment. We formulate the density operator approach for dynamical systems with non-Hermitian Hamiltonians, and derive a master equation that describes the statistical ensembles of EM wave modes. The method provides a theoretical instrument which can be used when designing the next generation of quantum EM devices for sensitive and non-invasive measurements.