International Research Symposium on Pure and Applied Sciences (IRSPAS)
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Item Analysis of a stochastic predator-prey model(Faculty of Science, University of Kelaniya, Sri Lanka, 2016) Prasadini, K.D.S.; Mallawa Arachchi, D.K.In biological systems Lotka-Volterra predator-prey model describes the population dynamics of two interacting species of predators and its preys. Classical predatorprey model is a primitive deterministic model governed by the two differential equations, namely, ���� = (������ − ��������) ���� and ���� = (�������� − ������) ���� where �� and �� denote prey and predator respectively, and ����, ����, ���� and ���� are parameters. This model can be improved by introducing stochasticity that accounts for the random fluctuations of a realistic predator-prey dynamical system. In this research work, we use Stochastic Differential Equation (SDE) approach. There are various ways, based on various assumptions, to incorporate SDE. One common approach is to use equations of the following form: ���� = (������ − ��������) ���� + ��(���� + ����)�� ������ ���� = (�������� − ������) ���� + ��(���� + ����)�� ������ These types of Stochastic Differential Equations (SDE) can be simulated in Matlab using numerical methods such as Euler-Maruyama method. Phase planes of the deterministic and stochastic models are carried out to demonstrate the behavior of this modified model. Our initial goal is to compare different stochastic models with the original deterministic model through simulations. The deterministic model has a positive equilibrium which is globally stable for positive values of the parameters. Nevertheless, in the stochastic model, the predator and prey populations may tend to extinction. Extinction percentages of predator or prey population are summarized and analyzed through this research work.Item Categorizing T20 cricket grounds(Faculty of Science, University of Kelaniya, Sri Lanka, 2016) Pathirana, O.D.R.; Mallawa Arachchi, D.K.T20 cricket matches are played by all cricket playing countries. There are more than 80 grounds in various countries on which these games are played. It is hypothesized that some of these grounds favor batsmen while others favor bowlers, or some grounds are high-scoring while others are low-scoring. In this research work, we perform a statistical analysis to determine whether those grounds can be categorized based on the past data. Numerous factors can be considered for the analysis. Main factors we have been considering are the total runs scored in both innings, humidity level, gust, wind, air pressure and the temperature at the grounds when the matches are played. Cluster analysis was used in investigating and determining the number of categories. This study helps identify the behavior of the T20 cricket grounds all over the world and thus enables one to predict the winning possibilities. Data were collected through Cricinfo website from 84 cricket grounds throughout the world. Ward’s method of Hierarchical cluster analysis, which is a major statistical method used in determining the relatively homogeneous clusters, was used. We found that grounds can be clustered into 3 clusters according to the coefficients of the Wards linkage table. When we consider the countries in which these grounds are located, there is no evidence to conclude that grounds in some specific countries are belonging to a particular category. For example there are grounds in India belonging to all three categories. SPSS statistical software was used in this analysis to categorize the grounds. The research work is being carried out to identify how cluster changes with different factors.Item Analysis of a stochastic predator-prey model(Faculty of Science, University of Kelaniya, Sri Lanka, 2016) Prasadini, K.D.S.; Mallawa Arachchi, D.K.In biological systems Lotka-Volterra predator-prey model describes the population dynamics of two interacting species of predators and its preys. Classical predatorprey model is a primitive deterministic model governed by the two differential equations, namely, = ( − ) and = ( − ) where and denote prey and predator respectively, and , , and are parameters. This model can be improved by introducing stochasticity that accounts for the random fluctuations of a realistic predator-prey dynamical system. In this research work, we use Stochastic Differential Equation (SDE) approach. There are various ways, based on various assumptions, to incorporate SDE. One common approach is to use equations of the following form: = ( − ) + ( + ) = ( − ) + ( + ) These types of Stochastic Differential Equations (SDE) can be simulated in Matlab using numerical methods such as Euler-Maruyama method. Phase planes of the deterministic and stochastic models are carried out to demonstrate the behavior of this modified model. Our initial goal is to compare different stochastic models with the original deterministic model through simulations. The deterministic model has a positive equilibrium which is globally stable for positive values of the parameters. Nevertheless, in the stochastic model, the predator and prey populations may tend to extinction. Extinction percentages of predator or prey population are summarized and analyzed through this research work.