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
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.
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