5. Stability and bifurcation
In this paragraph, we propose to further systematize the notions of stability and bifurcation already encountered in the previous paragraphs, adding a few more characteristic examples to those already mentioned.
5.1 Stabilities
A distinction will be made between asymptotic stability and structural stability, omitting a number of subtleties that are unnecessary in the present context.
A given dynamical system (underlying equations assumed fixed) is said to be asymptotically stable with respect to a state E if any solution close to E tends towards E when t ® ∞. The state E is then an attractor, characterized by a basin of attraction formed by all initial conditions that converge asymptotically to E. The classical...
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Stability and bifurcation
Characterization
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