Math 2250-4Fri Apr 199.2-9.3 Nonlinear systems of first order differential equations, with an emphasis on autonomous systems of two first order DEs. Linearization at equilibrium points and stability.We're discussing autonomous systems of two first order differential equations for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSIsRidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJ5RidGL0YyRjVGPQ==: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're interested in equilibrium solutions, stability, linearization, and the connections to phase portraits.\302\267 On Wednesday we linearized a competition model from ecology in order to understand solutions near an interesting equilibrium point. We did the linearization "the long way", and started talking about Jacobian matrix shortcut. \302\267 Finish that discussion and the last two class exercises there, using Wednesday's notes.For future reference, in case you need it to help with homework, here is the "long way":JSFHWe were considering the competition 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 .The point 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 is an equilibrium point, and we consider solutions near this equilibrium point, and write LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSIsRidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJ2RidGL0YyRjVGPQ== for the deviations of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSIsRidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJ5RidGL0YyRjVGPQ== from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW5HRiQ2JFEiNEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR1EldHJ1ZUYnLyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUYsNiRRIjZGJ0YvRi8= respectively:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjRGJ0Y5LUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GVy1GLDYlUSJ1RidGL0YyRjk= equivalently LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKCZtaW51cztGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjRGJ0Y5LUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjc3Nzc3OGVtRicvRk5GVy1GLDYlUSJ1RidGL0YyRjk=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjZGJ0Y5LUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GVy1GLDYlUSJ2RidGL0YyRjk= equivalently 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 . 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 . So, for example, as long as 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 then the linearized 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 the exact rates of change for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEidkYnRi9GMkY5 correct to within an accuracy no worse than 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, which is less than a hundredth the size of each of the linear terms in the DE.As we work through examples, we will be understanding that there is a fairly short list of possibilities for how the linearized solutions behave. Except in borderline cases (see Theorem on following pages) the stability properties and geometric pictures for the linearized DE's govern what happens in the non-linear problem as well. After going through the stability analysis for the equilibrium solutions in our Friday competition example we will understand:\302\267 In case the matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= for the linearized system is diagonalizable with real number eigenvalues, the linearized system for 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has general 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 .If each eigenvalue is non-zero, the three possibilities are: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 1) Verify how the two eigenvectors of the matrix LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= in the linear system show up in the three phase portraits above. (By the way, in the nodal cases, if the eigenvalues are equal then all solution trajectories follow rays from the origin, and the nodes are called "proper" nodes, as opposed to the case with unequal eigenvalues, in which case they're called "improper" nodes.Remark: In case LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJy1JI21vR0YkNi1RKCZ0aW1lcztGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZGLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlVGOkYyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ is not diagonalizable, then the single eigenvalue LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1 must be real, and its eigenspace must only be one-dimensional. In this case one can check that the general solution to the linearized system 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where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2KFEidkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lKnVuZGVybGluZUdGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRicvRjdRJ25vcm1hbEYn is the eigenvector for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y1 and 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 . Qualitatively the phase portraits look like those of improper stable or unstable nodes, depending on whether LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIjxGJ0Y1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGWS1GOzYkRkRGNUY1 or LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEnJiM5NTU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnRjUvRjNRJXRydWVGJy9GNlEnaXRhbGljRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIj5GJ0Y1LyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGWS1GOzYkRkRGNUY1 .Complex roots!Exercise 2) Consider this predator-prey model from section 9.3, for interacting populations LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSIsRidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJy1GLDYlUSJ5RidGL0YyRjVGPQ==. The population LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== is the prey (e.g. rabbits), and the population LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== is the predator (e.g. foxes).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2a) Discuss the various terms in this autonomous system of DEs. In this case there is good justification to use terms proportional to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJ5RidGL0YyRjk= to model how these populations interact. Explain.2b) Find the equilibrium solutions, classify the two with real eigenvalues, and sketch the phase portrait for the linearized problem.2c) The equilbrium solution in the first quadrant is especially interesting. Linearize the system at this point and find the eigenvalues. They will be complex....and we know this leads to spiral phase diagrams (or elliptical if the eigenvalues are purely imaginary.) Rather than doing the painful computation of the general solution to the linearized 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 plot several values of the tangent vector field along the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIixGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRiw2JVEidkYnRi9GMkY5 axes to deduce whether the spirals are clockwise or counterclockwise, and their rough shape.2d) Compare your work to the pplane phase portrait on the next page, and interpret your work in terms of the predator-prey model.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 discussion of complex eigenvalues for linear homogenous systems of two first order DE's: Let LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJy1JI21vR0YkNi1RKCZ0aW1lcztGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZGLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRlVGOkYyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJ0Y+ have complex eigenvalues 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 . For 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 let the eigenvector be 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. Then we know that we can use the complex solution 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 to extract two real vector-valued solutions, by taking the real and imaginary parts of the complex 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 .Thus, the general real solution is a linear combination of the real and imaginary parts of the solution above: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 .We can rewrite LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KFEidUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lKnVuZGVybGluZUdGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ0RidGMi9GN1EnaXRhbGljRicvRjdRJ25vcm1hbEYnRkZGRg== 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 .Write the inside coefficient of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2KFEiYUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lKnVuZGVybGluZUdGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRicvRjdRJ25vcm1hbEYn in amplitude-phase form:LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRi82JVEkY29zRicvRjNRJmZhbHNlRidGPi1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYvNiVRInFGJ0YyRjUtSSNtb0dGJDYtUSJ+RidGPi8lJmZlbmNlR0ZHLyUqc2VwYXJhdG9yR0ZHLyUpc3RyZXRjaHlHRkcvJSpzeW1tZXRyaWNHRkcvJShsYXJnZW9wR0ZHLyUubW92YWJsZWxpbWl0c0dGRy8lJ2FjY2VudEdGRy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRl5vLUYvNiVRInRGJ0YyRjVGPkY+LUZRNi1RIitGJ0Y+RlRGVkZYRlpGZm5GaG5Gam4vRl1vUSwwLjIyMjIyMjJlbUYnL0Zgb0Zoby1GLDYlRi4tRiM2JC1GOzYkUSIyRidGPkY+RkAtRi82JVEkc2luRidGRkY+RkgtRlE2LVEiPUYnRj5GVEZWRlhGWkZmbkZobkZqbi9GXW9RLDAuMjc3Nzc3OGVtRicvRmBvRmhwLUYvNiVRIkNGJ0YyRjVGUEZDLUZJNiQtRiM2KEZNRlBGYW8tRlE2LVEoJm1pbnVzO0YnRj5GVEZWRlhGWkZmbkZobkZqbkZnb0Zpby1GLzYlUScmIzk0NTtGJ0ZGRj5GPkY+Rj4=with, as we know for amplitude-phase form: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.Thus, the inside coefficient of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2KFEiYkYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lKnVuZGVybGluZUdGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRicvRjdRJ25vcm1hbEYn 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 .So we can rewrite LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KFEidUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lKnVuZGVybGluZUdGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ0RidGMi9GN1EnaXRhbGljRicvRjdRJ25vcm1hbEYnRkZGRg== 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 .LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2KFEidUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lKnVuZGVybGluZUdGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ0RidGMi9GN1EnaXRhbGljRicvRjdRJ25vcm1hbEYnRkYtSSNtb0dGJDYtUSI9RidGRi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGTi8lKXN0cmV0Y2h5R0ZOLyUqc3ltbWV0cmljR0ZOLyUobGFyZ2VvcEdGTi8lLm1vdmFibGVsaW1pdHNHRk4vJSdhY2NlbnRHRk4vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Znbi1GLDYlUSJDRidGMkZELUZJNi1RIn5GJ0ZGRkxGT0ZRRlNGVUZXRlkvRmZuUSYwLjBlbUYnL0ZpbkZhby1JJW1zdXBHRiQ2JS1GLDYlUSJlRidGMkZELUYjNiYtRiw2JVEicEYnRjJGREZdb0ZBRkYvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUY9NiQtRiM2L0Zdb0Zdby1GLDYlUSRjb3NGJy9GM0ZORkYtRj02JC1GIzYoLUYsNiVRInFGJ0YyRkRGXW9GQS1GSTYtUSgmbWludXM7RidGRkZMRk9GUUZTRlVGV0ZZL0ZmblEsMC4yMjIyMjIyZW1GJy9GaW5GZHEtRiw2JVEoJmFscGhhO0YnRmhwRkZGRkZGRl1vLUYsNihRImFGJ0YvRjJGNEY2RjktRkk2LVEiK0YnRkZGTEZPRlFGU0ZVRldGWUZjcUZlcS1GLDYlUSRzaW5GJ0ZocEZGRmlwLUY9NiQtRiM2JS1GSTYtUSomdW1pbnVzMDtGJ0ZGRkxGT0ZRRlNGVUZXRllGY3FGZXEtRiw2KFEiYkYnRi9GMkY0RjZGOUZGRkZGXW9GXW9GRkZGRkY=Thus LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2KFEidUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lKnVuZGVybGluZUdGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUSJ0RidGMi9GN1EnaXRhbGljRicvRjdRJ25vcm1hbEYnRkZGRg== traces out a stable spiral ("spiral sink") if LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIjxGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= , and unstable spiral ("spiral source") if LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= , and an ellipse ("stable center") if LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= 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Let 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 be an equilibrium point for a first order autonomous system of differential equations. (i) If the linerized system of differential equations at 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 has real eigendata, and either of an (asymptotically stable) nodal sink, an (unstable) nodal source, or an (unstable) saddle point, then the equilibrium solution for the non-linear system inherits the same stability and geometric properties as the linearized solutions.(ii) If the linearized system has complex eigendata, and if LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEoJiM4NDc2O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLDYlUScmIzk1NTtGJ0YvRjJGMkYyLUkjbW9HRiQ2LVElJm5lO0YnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRjJGMg== , then the equilibrium solution for the non-linear system is also either an (unstable) spiral source or a (stable) spiral sink. If the linearization yields a (stable) center, then further work is needed to deduce stability properties for the nonlinear system.Example 3) Consider this predator-prey model, which is a variation from the previous example - the prey population (rabbits) is now "exponential growth" rather than "logistic", and the predator population (foxes) keeps the same "exponential decay" dynamics: 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It is straightforward to verify that there are two equilibrium solutions: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkobWZlbmNlZEdGJDYkLUYjNictSSNtbkdGJDYkUSIwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEifkYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GODYtUSIsRidGNEY7L0Y/USV0cnVlRidGQEZCRkRGRkZIRkovRk5RLDAuMzMzMzMzM2VtRidGMEY0RjRGTy1GLDYkLUYjNiYtRjE2JFEiNUYnRjRGTy1GMTYkUSMxMEYnRjRGNEY0RjQ= . In your homework you will verify that for the linearized problem, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobWZlbmNlZEdGJDYkLUYjNiYtSSNtbkdGJDYkUSI1RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JFEjMTBGJ0Y0RjRGNEY0 is a stable center....which is the borderline case - more work is needed to determine whether or not the equilbrium point is stable for the original non-linear system. It turns out that it is. You will investigate that in this weeks homework problem. This sort of dynamics leads to credible explanation of how fisheries may periodically collapse and then recover (prey = fish, predators = 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