Eigenvalues and eigenvectors is one of the important topics in linear algebra. The purpose of this assignment is to study the application of eigenvalues and eigenvectors in our daily life. They are widely applicable in physical sciences and hence play a prominent role in the study of ordinary differential equations. Therefore, this assignment will provide explanations on how eigenvalues and eigenvectors will be functional in a prey-predator system. This will include background, history of the concept and explanation on what is meant by eigenvalues, eigenvectors and prey-predator system. Other than that, models and application of the eigenvalues and eigenvectors in prey-predator system will also be included in this assignment. Necessary appendix such as graphs will be attached with the assignment.
BACKGROUND AND CONCEPT
Linear algebra is the study of linear transformations of linear equations which are represented in a matrix form by matrices acting on vectors. Eigenvalues, eigenvectors and Eigen space are properties of a matrix (Sharma, n.d.). The prefix “Eigen” which means “proper” or “characteristics” was originally developed in German and invented by a German mathematician. Latent roots, characteristic roots, proper values or characteristics value are few common terms of eigenvalues. They are a special set of scalars allied with a linear system of equations for instance a matrix equation. In engineering and physics field, knowledge about eigenvalues and eigenvectors are very crucial where it is corresponding to diagonalization of matrix. They are practice in vibrating system with small oscillations, concepts of rotating bodies, as well as stability analysis. Corresponding eigenvectors will be paired with their eigenv...
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Trophic Links: Predation and parasitism. (2005, February). Retrieved March 14, 2014, from http://www.globalchange.umich.edu/globalchange1/current/lectures/predation/predation.html
Weisstein, E.W. (n.d.). Eigenvalue. Retrieved March 14, 2014, from http://mathworld.wolfram.com/Eigenvalue.html
APPENDICES
The graph shows that matrix A acts by stretching the vector x, not changing its direction, so x is an eigenvector of A.
The above picture illustrates the prey-predator relationship.
This pictures demonstration the level of food chain in the ecosystem. The bottom level is the producer and the higher level will be the predator.
This indicates changes in numbers of the hare and throughout the years.
This diagram shows the Lotka-Volterra model of solving prey-predator problem.
1) Inspiration: Grey wolves are considered as apex predators, meaning that they are at the top of the food chain. Grey
Morgan, Sally. Chapter 6.1: Feeding the World. The New Encyclopedia of Science: Ecology and Environment. 2003. 21 Feb 2008.
Many people have tried many diets to eat healthy. In The Omnivore’s Dilemma, Michael Pollan talks about the different food chains that many people think should be used. The food chains are industrial, which is like processed meat (like in fast food places). Next is the industrial organic food chain, this food chain is when the food is grown safely, but are shipped thousands of miles and uses a lot of fossil fuels. Then there is the local sustainable food chain, where the food is grown safely and the people have to actually go to the farm to get the vegetables that they want. Lastly, it is the hunter-gatherer food chain, which is basically the the people have to make the meal themselves. People have to kill their own meat and hunt for their
The different types of components of an ecosystem are connected. it is very important to know, because a change in the amount of abiotic resources available or a change in the size of anyone in a certain population of organisms can have impact on the size of the other populations found in that ecosystem. Also the interactions that take place between the organisms that are found in an ecosystem can change the characteristics of some populations. One example that characteristics can be influenced by population interactions include the proportion of individuals within a population to have a specific traits or the average height or weight of the members of that population. One type of interaction that can result in a change in the characteristics of a population is a predation. It often has strong influence on the characteristics of a prey population. biologist study how the characteristics of a specific prey population change in the response to a specific type of predation and to understand how different types of interactions can result in a change in the characteristics of a population.
Multiscale PCA (MSPCA) combines the capability of PCA to extract the cross-correlation between the variables and wavelets to divide deterministic features from stochastic processes and approximately de-correlate the autocorrelation among the measurements. Figure 2.3 illustrates the MSPCA procedures.
The authors of this article are David Tilman and Jason Hill. David Tilman is a Regents Professor and McKnight Presidential Professor of Ecology at the University of Minnesota. Tilman is interested in “the benefits that society receives from natural and managed ecosystems and in the ways to assure environmental and social sustainability in the face of global increases in human consumption and population.” He has also written many scholarly articles and books on resource and plant competition and on biofuels. Tilman is very knowledgeable in his field of study; therefore, we can most certainly take his word for everything he talks about in this article.
Introduction back to outline Ecosystem instability is obvious through the depletion of our natural food webs. There are many places to look to find these obvious problems. One example would be the lack of apex predators that has caused explosions in populations of the "prey" animals. Usually this is a result of some kind of human involvement. Along with the lack of apex predators has come the infestation of foreign animals. These "foreign invaders" are usually transported from their native land to a foreign country by human transport vessels. What then is our role in solving these population problems? There are many options, but how do we know what is right?These questions are complicated but they can be answered. You can look at it the same way one looks at a math problem. Before one tries to solve some kind of complicated situation, the background and surrounding information must be known. In other words, to begin trying to solve our ecosystem problems, we must first and foremost understand the ecosystems themselves. With out the knowledge of how the ecosystem functions naturally there is no way to try and resolve some of the current situations. Trying to resolve situations now without knowing the ecosystem...
...food web or food chain that is made up of producers, herbivores, consumers, and omnivores. Food webs show the connections animals have with each other on who eats whom. The Amazon has many species of animals that are all connected somehow but using only a small handful of producers and consumers can make it easier to understand and show how they are connected in some way. A macaw and a fruit bat eat orchids but the emerald tree boa will soon eat macaw and the fruit bat. Across the Amazon, a spider monkey can be eating from a banana tree or the jaguar will eat the Bengal bamboo then the spider monkey. Soon the jaguar can be patiently waiting for the next victim, which will be a parrot that is eating off the same banana tree, as the spider monkey was not long ago. Every animal is connected somehow and creating a food web is the best way to show and easy to understand.
Purpose: The purpose of this lab is to investigate the various components of different ecosystems in a smaller representation and study the conditions required for the ecosystem’s sustainability as well as the connections between
This would be food chains. Food chains are a key part in any wildlife around the world. They are a system that shows what eats what from the plant-small prey-Large predators. In our lakes smaller fish eat aquatic plants , the smaller fish are eaten by larger predators and so on. But if one part of the food chain is messed up, like if all of the large predatory fish were fished out, there would be nothing to eat the small prey fish. This would cause the small prey fish to overpopulate and more mouths to feed. This would cause the aquatic plant population to decline. Now you see how one slight change of a part of a food chain can screw everything up. Which brings us to our next
There are many types of ecosystems”Some are them are immense biomes and other can be minor ecosystems like a puddle or a tree trunk”, but wouldn't it be amazing too have a ecosystem the size of a pop bottle. Luckily this is not a hallucination Ecosystems like these are called ecocolumn which are basically a simulation of a medium ecosystem synce it contains a small aquarium on the bottom and a terrarium in the top. By doing these we are going to be able to see the relationships between the consumers, producers and decomposers, In these case the decomposer can be the earthworm the consumers can be the fish and the producers can be the plants these organism are characterized in these category because of their symbiotic relationship. In a Ecocolumn
How Will I Use Math in Everyday Life All throughout the days I spent in school sitting in math class learning Algebra, Geometry, and the various other math courses, I pondered whether or not I would ever even use these math skills in my life. The sad truth is that you will most likely use most of the math skills that you learned throughout high school in everyday life. There are honestly so many different ways you can use math in life, like buying a car, your weekly trip to the grocery store, and even at home. It honestly hurts you to not pay attention because you will in fact use math in your everyday life. There are many different ways that math is used at home, just like everywhere else.
On the second level, the introduced species starts to reproduce faster than other native species around it. It also out-competes native species for resources
In 1891, a German zoologist named Karl Semper introduced the concept of a food chain, a process that is requisite for all living creatures. The chain consists of different levels. On the bottom are plants, then herbivores, the animals that eat plants. Next are carnivores, animals that eat other animal species, and the last are the animals that eat carnivores. The chain tends to overlap due to animals that eat more than one kind of food. Some people choose to be carnivores, while others choose to be herbivores due to the feeling that it is wrong to eat another living being. Humans are usually thought of as the superior animals on the Earth and living in modern society many nutritious foods are provided, especially meat. Some people choose to live herbivorous lifestyles due to moral and ethic reasoning, which can easily result in malnutrition as well as health risks that could have easily been avoided had they eaten carnivorously.
I believe that the growing role of mathematics, science and technology in modern life demands that we, for our active participation in society, personal satisfaction and our working development we should not only be able to read and write but also, have the skills and knowledge in these areas. Before doing the readings I thought that being scientific and mathematic literal was to be able to solve math and science problems. My opinion changed drastically after reading each article and book on my reference list. Now I believe that it’s not only to be able to solve problems, but that being Scientific and Mathematic literal is to be able to communicate with others in our or in different areas of study, to think on the nature of a subject and work