On the foundations of bifurcation theory
Copyright policy )On the foundations of bifurcation theory
Persistence of absorbing property of sets is proved for perturbations of general semisystems in a metric space. The generalization of the persistence theorem for asymptotic stability of an invariant set is obtained, and sufficient conditions of a new type for occurrence of bifurcation of an invariant set are found. In particular, extension of results for the generalized Poincaré-Andronov-Hopf bifurcation to the systems of the type considered is obtained.
semidynamical systems, asymptotic stability, absorbing sets, Local and nonlocal bifurcation theory for dynamical systems, bifurcation, persistence theorem
semidynamical systems, asymptotic stability, absorbing sets, Local and nonlocal bifurcation theory for dynamical systems, bifurcation, persistence theorem
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