(1Consider the interaction of two species of animals in a habitat. We are told that the change of the populations x(t) and y(t) can be modeled bythe quationsFor this system, the smaller eigenvalue isSymbiosisdxdtdydt= 0.8x + 2y,=1. What kind of interaction do we observe?3x + 2.22044604925031e 16y.and the larger eigenvalue is[Note-- you may want to view a phase plane plot (right click to open in a new window).]If y = Ay is a differential equation, how would the solution curves behave?A. All of the solutions curves would converge towards 0. (Stable node)B. All of the solution curves would run away from 0. (Unstable node)C. The solution curves would race towards zero and then veer away towards infinity. (Saddle)OD. The solution curves converge to different points.

The system of equation is as follows:To Find:The smallest and largest eigenvalue.

Answered: (1 Consider the interaction of two…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(1 Consider the interaction of two species of animals in a habitat. We are told that the change of the populations x(t) and y(t) can be modeled by the quations For this system, the smaller eigenvalue is dx dt dy dt = 0.8x + 2y, = 3x + 2.22044604925031e - 16y. and the larger eigenvalue is