LIFESCI 30B Lecture 27: Lectures 27 - 28
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The big conclusion from the past: 3 days lectures : To analyze equilibrium points of a system of differential equations : The equilibrium points : set f ( x ,yl=o. Steps : for each equilibrium point ( x* , y* ) do the following a . To classify the type of eq . point . < 0 then unstable source ) then stable ( sink ) > 0 then unstable spiral complex w| real part. Jacobian ( linear approximation ) to classify the. 0 or the eigenvalues are complex with real part =0( pure imaginary) or repeated eigehvalves , then this testisincondus. ve. You can do this with more than two variables n v@c@ Stale space further away , the trajectories are all spiraling in toward it . Stable spiral eq . point changes to an unstable spiral ( override ) Optimization : given a function f ( ,y , Z find the values ot the variables: y ,
