5.0 A better way to understand Differential Equations | Nonlinear Dynamics | Bendixson's Criterion

Series1: Part 1: https://youtu.be/ySfs8YVMY7Q Part 2: https://youtu.be/I9UEBRya4X0 Part 3: https://youtu.be/6mLCFyEv3Z0 Series 2: Part 4: https://youtu.be/wZvFKcQ_3Rc Bendixson'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 Music: Let's Rock Today by Dmitrii Paderin