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Unformatted text preview: x (0) = 4 ,y (0) = 4 . (d) Draw the x- and y-nullclines and the direction arrows in the phase plane. (e) Sketch the solution curve for the initial condition in part (c) into the phase plane. (f) Is the point (0,0) stable or unstable? Classify this equilibrium. 4. Consider a disease that propogates according to the system dx dt = 16-. 2 xy-. 4 x dy dt = 0 . 1 xy-8 y 1 where x represents susceptible individuals, y represents infected individuals. (a) Find all biologically meaningful steady states. (b) Show that the Jacobian matrix of this system is given by ±-. 4-. 2 y-. 2 x . 1 y . 1 x-8 ² (c) For the biologically meaningful steady states from (a), ﬁnd the eigenvalues of the Jacobian matrix. (d) Determine the stability of the biologically meaningful steady states. 2...
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- Winter '07
- Matrices, Trigraph, Eigenvalue, eigenvector and eigenspace, Jacobian