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\n5.0 A better way to understand Differential Equations | Nonlinear Dynamics | Bendixson's Criterion\n

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\nBendixson's criterion is another method used to disprove the existence of closed orbits. A periodic solution is a type of closed orbit. This theorem only holds for simply connected regions in 2D. The statement is that if on a simply...\nBendixson's criterion is another method used to disprove the existence of closed orbits. A periodic solution is a type of closed orbit. This theorem only holds for simply connected regions in 2D. The statement is that if on a simply connected region, the divergence of the vector field, div([f(x,y); g(x,y)]) , is not identically zero and does not change sign then there are no closed orbits lying in that domain. Dulac's criterion (not covered in this video) is a generalization of this method. Chapters: 0:00 Last time 0:40 Intro 0:50 Recap 2:20 Flux Integral 3:13 Divergence Theorem 4:17 No Periodic Orbits 5:24 Example 6:33 Up Next 6:53 Outro\n
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Resource Details

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Media Length
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6:48
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Grade
Higher Ed
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Subjects
Math
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Instructional Videos
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\nVirtually Passed\n\n
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Date
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2023
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Language
English
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For Teacher Use
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Fine Print: Educational Use
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vector, time
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nonlinear dynamics, bendixson, periodic orbits, linearization, differential equation, stuff inside, closed curve, double integral, partial derivative, equation, curve, integral, partial, term, talked, exist, give, turns, disprove, existence, talk, started, hard, make, equal, function, point, system, true, trajectories, familiar
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