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Modelling and simulation using stella
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Modelling and simulation using stella Modelling and simulation using stella Document Transcript

  • 1.0 Introduction 1.1 Simulation TheoryModel is a representation of an object, a system or an idea in some form other than that of theentity itself (Shannon). Types of model are divided into two, which are physical andmathematical. Physical model is like scale models and prototype plants while mathematicalmodel is like analytical queuing models, linear programs and simulation. A mathematical model is an abstract model that uses mathematical language todescribe the behaviour of a system. Mathematical models are widely used in the naturalsciences and engineering such as biology, physics and electrical engineering. These modelsare also used in the social sciences such as sociology, political sciences and economy. Thefrequent users of these models are physicist, engineers, computer scientists and economists. A simulation of a system is the operation of a model, which is a representation of thatsystem. The model is amenable to manipulate which would be impossible, too expensive, ortoo impractical to perform on the system and attempts to simulate an abstract model of aparticular system. The operation of the model can be studied by the user. From this, theproperties related to the behaviour of the actual system can be concluded. One of the main advantages of using simulation in teaching and learning is theprocess of teaching and learning becomes more interesting and exciting as the learners canexplore everything in various types of experiments. If they have the software of simulation,they can explore it early when they are not in the class. These can make them more inspiringto study and discover a new thing. Besides, simulation also can help the teachers to teach theabstract content to the students. It is meant that, the simulation can make the student easy tounderstand as they can use the simulation and not just imagine on what have been taught bythe teacher. Other advantages of using simulation are very quick development of complexmodels, short learning cycles and no programming is needed. So, only minimal errors willoccur. However, this simulation also can give disadvantages to the students that do not havecomputer or limited availability of computers. They will not have the opportunity to exploreafter they have learnt in the class. Their learning process will happen only in the class. Inaddition, this simulation also can give a big problem to the users that do not know how to use 1
  • computer. The users need to do two things in one time, which are learning about thecomputer and also learning about the simulation. So, may be the user will be lag behind theothers. Besides, many simulations require intensive pre simulation lesson preparation. So, ittakes time if we want to use the simulation in a short period. High cost of software alsoinclude as the disadvantage of the simulation. Only the trial one can be used by the users.But, after 30 days, it cannot be use anymore. In addition, limited scope of applicability andalso limited flexibility. This is because the variation of the topics is not too many. Some ofthem may not fix with the users specific. 1.2 STELLA Software STELLA is a new software program that has been developed to enable very broad,non technical audiences to conceptualize, construct and analyze system dynamic models. Oneof the goals of the development of STELLA is to enhance the learning process. This softwareoffers a practical way to visualize and communicate how complex and ideas really work. Itconsists of endless questions, which make the users more attracted to use it. As this softwareis easy to use, it has been used widely in education from economics to physics, chemistry topublic policy and literature to calculus. This model allows the user to communicate how asystem works. Generally, STELLA software is really useful for the visual learners becausethe animation, diagram and charts in that software can help them discover the relationshipbetween variables in an equation. While for verbal learners, visual models with words aremore suitable for them. STELLA is being used to stimulate a system over time, jump the gap between thetheory and the real world as the simulation is closely like the real one, enable students tocreatively change the systems by changing the value or variables, teach the students to lookfor the relationships by seeing a big picture and clearly communicate system inputs andoutputs and demonstrate outcomes. 1.3 Experiment Theory STELLA has been used in the experiment of Predator-Prey Dynamics. Predator-preytheory is traced from its origin in the Malthus-Verhulst logistic equation, through the Lotka-Volterra equations, logistic modification to prey and predator equations, incorporation of theMichaelis-Menten-Holling functional response into the predator and prey equations and the 2
  • recent development of ratio-dependent functional responses and per capita rate of changefunctions. In the study of the dynamics of a single population, we always take into considerationsuch as factors of natural growth rate and the carrying capacity of the environment. In thisexperiment, we study an interaction between two species, which are prey and predators. Preyis the species that has been eaten while predator is the species that eats the others. Predation is only one of several agents that cause population cycles. Other factors thatcontributed in the population cycles are mass emigration, genetic changes in the populationand physiological stress due to overcrowding. Population cycles are difficult to achieve in thelaboratory. Usually, the predators search out every one of the prey and then they go toextinction due to lack of food. The predator-prey model may be stabilized by making two assumptions about thegrowth rates of the prey and also about the growth rates of the predator. If the preys orpredators are destroyed at the same rate by some outside agent, the prey will proportionallyincrease and the predators will proportionally decrease. This is because the birth rate of theprey is not affected, the death rate of the prey is reduced and the birth rate of the predator isreduced.2.0 Content This STELLA software provides three parts for the users, which are background andcontent of the experiment in details, explore the model and experiment. So, as we want toconduct an experiment about predator and prey, we can choose the last part, which isexperiment. Before we choose that part, we can read the background first in order to knowwhat is the experiment tells about. Background of this experiment tells that predator-prey oscillations are common inmany simple ecosystems. According to Odum’s classic ecology textbook, interesting andonly partly understood density variations are those which are not related to seasonal orobvious annual changes, but which involve regular oscillations or cycles of abundance withpeaks and depressions every few years, often occurring with such regularity that thepopulation size may be predicted in advance. The best known cases concern mammals, birds,insects, fish, and seed production in plants in northern environments. Among the mammals, 3
  • the best-studied examples exhibit either a 9- to 10- year or 2- to 4- year periodicity. A classicexample of a 9- to 10- year oscillation is that of the snowshoe hare and the lynx. The background also tells us about the purpose of this experiment despite of thepredator and prey. After we have read the background, we can conduct the experiment. Theinterface of this simulation will show all of the variables involved. For this experiment, thesize of one time lynx harvest is the manipulated variable while, years is the respondingvariable. There are few buttons that we can click in order to see how the simulation isfunctioning. The buttons are ‘run’, ‘pause’, ‘stop’ and ‘reset’. All of the button can be click tosee what will happen to the simulation software. Exploring is important before we start toconduct the experiment. In order to start the experiment, ‘run’ button should be click. But, ifwe want to cancel it, we can click the ‘reset’ button. 4
  • For the beginning, we click the ‘run’ button without changing any value in order toknow what graph will be produce. Then, we can see that only straight lines are produced forboth hares and lynx. We need to note that the lynx birth rate depends upon the food supplyavailable, which is the hares and the death rate of the lynx is not dependent on the hares’density. This graph shows that the amount of the prey and predator are constant along theyears. This does not mean that no interaction is occurred, but this is meant that the conditionfor this interaction is stable. The amount of hares is the same as the amount of lynx dead. Asthe lynx dead, so the amount of hares will not be reduced because they are not being eaten. This step is to demonstrate to the student on how to use this simulation and see therelationship among the variables on the graph. This simulation enables them to know the wayscientists do their work. This simulation can make the students more interested to conduct an 5
  • experiment because they are able to change the values to any value that they want and seewhat the result is. Students should predict and explain the outcomes that they expect the simulation togenerate. From that, the students will not stay passively in the class experiment. Every effortshould be make it difficult for them to become passive. Each student must submit timelyinput and not rely on classmates to play for them. So, everyone will have the experience ofusing the simulation. After changing the value of size of one time lynx harvest to 160, the graph has shownfluctuation. Here, it shows that the amount of the lynx is depending on the amount of thehares. If the amount of hares is increase, the amount of the lynx will also increase. If thehares decrease, the lynx also decrease. But, the graph shows straight line at the beginning. Atthis point, there is no interaction yet. 6
  • This simulation has the potential to engage students in deep learning that empowersunderstanding compared to the surface learning that requires only memorization. From thissimulation, students will more understand as they conduct the experiment by themselves andfind the relationship between the variables in order to get the conclusion of the interaction. Ifthey did not use this simulation, they maybe not understand, but they only memorize what theteacher has taught them. According to the pattern of the graph, the students are able to predict what willhappen on the next years as they know already what the pattern is. If the rate of prey isdecreasing, the rate of predator is also decreasing. And if the rate of prey is increasing, therate of predator is also increase. Then, we change the value of the size of one time lynx harvest to 380. This amount isdoubled to the value for the first trial, which is 160. So, the fluctuation of this graph alsoshows doubled height of the first trial. Here, the students can see how the graph changeswhen the value is changed. The students can understand and predict the graph along the yearsas the pattern of the fluctuation is just the same from the beginning to the end. 7
  • By using this simulation, the students can think more about what will happen next andwhat are the factors that can cause the pattern of the graph. The students also can develop afeel for what variables are important and the significance of magnitude changes inparameters. If the magnitude is change, the graph will also change. There is no such thingthat the value is change, but the graph still the same. This simulation also can help the students to understand the probability and samplingtheory. The teachers not have to worry the validity of this simulation theory becauseinstructional simulations have proven their worth many times in the statistics based fields. So,it can be said that simulation is one of the best method for the teachers to give their studentmore understanding in the abstract topics. When we change the value of the size of one time lynx harvest to the maximum value,which is 750, this graph is shown. Specifically, increasing in the prey population will causethe predator birth rate to rise and thus increase their population. Then, the prey death rate willrise. This graph shows a typical plot produced from that situation. Here we can see thecharacteristics of cyclical fluctuations between the hares and the lynx. 8
  • When we look at the pattern of the graph, we noticed that the lynx’s pattern is closelyfollows the hares’ pattern but the lynx’s peaks and valleys happen a bit after the hares’ peaksand valley. This interaction is complex. Disease, food supply and other predators arevariables in this complex interaction. The flux in this cyclic relationship is what allows forthe ecosystem dynamic to work. Every ten years or so, the hares’ reproduction rate increases. As more hares are born,they eat more of their food supply. The lynx population size also begins to increase becausehares are their food. As this graph is more complex to be interpreted by the students, it can cause activelyengaging in student. They are actively participating to formulate new questions to be askedand also anticipating the outcomes. Social processes and social interactions in action are alsooccurred. They are also able to transfer knowledge to new problems and situations. A welldone simulation should be constructed to include an extension to a new problem or new setparameters that requires student to extend what they have learned in an earlier content.3.0 Conclusion Post simulation discussion with the students leads to deeper learning. So, theinstructor should: 1. Provide sufficient time for students to reflect on and discuss what they learned from the simulation. 2. Integrate the course goals into the post simulation discussion. 3. Ask the students explicitly such as ask how the simulation helped them to understand the course goals or how it may have made the goals more confusing. Simulation is suitable to be used in the school because it can motivate students inlearning. Simulation motivate students by keeping them actively engaged in the learningprocess through requiring that problem solving and decision making skills be used to makethe simulation run. As the simulation runs, it is modelling a dynamic system in which thelearner is involved. Thus, participation in simulations enables students to engage in systemsthinking and enhances their understanding of systems as well as of science concepts. 9
  • Simulation can be considered as a powerful tool in active learning experiences. It canprovide a kind of lab-like experiences. So, the students will become more exciting andinspiring in study because most of the students like to do something rather than just hearingto something. Finding a good simulation in teaching is a challenge for the teachers in order tointegrate them into the content and objectives of the course chosen. However, if the teachersknow what their students need, it is easier for them to choose a suitable simulation. STELLA is suitable to be launched in Malaysia as it is one of the simulations whichgive benefits to the users whether the user is a student or a teacher. Some of STELLAbenefits are: 1. The language increases the accuracy and clarity of verbal descriptions, ambiguities diminish and communication becomes much more efficient and efficient. 2. The software provides a check on intuition. 3. This software provides a vehicle for building an understanding of why. 4. The tools enable an easier operation and demonstration 10
  • ReferencesA. A. Berryman (1992). The Origins and Evolution of Predator-Prey Theory. Ecology. 73 (5). Retrieved from http://www.jstor.org/discover/10.2307/1940005?uid=373867 2&uid=21 29& uid=2&uid=70&uid=4&sid=21101509219257Peter Chesson (1978). Predator-prey Theory and Variability. Annual Revolution Ecology System. 9:323 (47). Retrieved from http://eebweb.arizona.edu/faculty/ chesson/Pete/ Reprints/ 1978_Predator-Prey%20Theory%20and%20Variability.pdfAnonymous (2002). Lynx-Hares Cycles. Retrieved November 25, 2012 from http://pzweb.harvard.edu/ucp/curriculum/ecosystems/s6_res_lynxhare.pdfAnonymous (1996). Effective Use of Simulations In The Classroom. Retrieved November 25, 2012 from http://www.clexchange.org/ftp/documents/Implementation/IM1996- 01EffectiveUseOfSims.pdfBarbara L. Peckarsky (2006). Predator-Prey Interaction. Retrieved November 25, 2012 from http://www.zoology.wisc.edu/faculty/peckarsky/pdf/CH24predprey.pdfMarshall W. Johnson (2000). Prey / Predator Interaction Models. Retrieved November 27, 2012 from http://nature.berkeley.edu/biocon/BC%20Class%20Notes/73-77%20 Predator%20Models.pdfMike Scott (2004). Data Modelling. Retrieved November 27, 2012 from http://www.liberty.edu/media/1414/[6330]ERDDataModeling.pdfIsee system (2012). STELLA System Thinking for Education and Research. Retrieved November 20, 2012 from http://www.iseesystems.com/softwares/Education/ StellaSoftware.aspxPeter Vescuso (2008). Using STELLA to Create Learning Laboratories: An Example From Physics. Retrieved November 26, 2012 from http://www.systemdynamics.org /conferences/1985/proceed/vescu964.pdfWilliam W. Murdoch (1971). The Developmental Response of Predators to Changes in Prey Density. Ecology. 52 (1) Retrieved from http://www.jstor.org/discover/10.2307/1 934744?uid=3738672&uid=2129&uid=2& ui d=70&uid=4&sid=21101509437847 11