5. Stability and bifurcation

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...