Charlotte Moser on Saddle-node Bifurcation

Nonlinear models:


My comment:

It was interesting how unresolved processes show up as noise. The first-order system has a discontinuous evolution at the tipping point, but presumably the first-order system is just an approximation to a higher-order system where those unresolved processes show up as a continuous evolution in a higher-dimensional phase space. I guess the maths for this sort of transition is much more complicated though.

Subscribe to Charlotte Moser. 

There is a whole course on Non-linear dynamics and chaos by Shane Ross. He mentions (2:50) discontinuities in phase-space topology on either side of a bifurcation point:

 

See Collaborative Mathematics.

 

Here's some more on phase space topology:

Subscribe to Dr Shane Ross.

Catastrophes, and Other Theories of Form – Beyond Networks: The Evolution of Living Systems

Subscribe to Johannes Jaeger. 

See also Mike Harms on Physical Models of Biological Processes. 

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