منابع مشابه
Explosions near Isolated Unstable Attractors
We describe the set of explosive orbits in the region of attraction of an unstable attractor which is isolated in the sense of C.C. Conley. Sufficient conditions are given for the existence of explosions in certain parts of the region of attraction and for an unstable attractor to have finitely generated integral Alexander-Spanier cohomology groups. Finally, we study the case of singularities t...
متن کاملStable and unstable attractors in Boolean networks.
Boolean networks at the critical point have been a matter of debate for many years as, e.g., the scaling of numbers of attractors with system size. Recently it was found that this number scales superpolynomially with system size, contrary to a common earlier expectation of sublinear scaling. We point out here that these results are obtained using deterministic parallel update, where a large fra...
متن کاملParametrizing Unstable and Very Unstable Manifolds
Existence and uniqueness theorems for unstable manifolds are well-known. Here we prove certain refinements. Let f : (C, 0) → C be a germ of an analytic diffeomorphism, whose derivative Df(0) has eigenvalues λ1, . . . , λn such that |λ1| ≥ · · · ≥ |λk| > |λk+1| ≥ · · · ≥ |λn|, with |λk| > 1. Then there is a unique k-dimensional invariant submanifold whose tangent space is spanned by the generali...
متن کاملUnstable attractors induce perpetual synchronization and desynchronization.
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which unstable attractors arise naturally. From random initial conditions, groups of synchronized oscillators (clusters) are formed that send pulses alternately, resulting in a periodi...
متن کاملPreserving Transients on Unstable Chaotic Attractors
In this chapter we present a controlling method which allows the preservation of transient chaotic evolution in the desired region of the phase space. The concept of practical stability for the perturbed chaotic attractors and the connection between practical and asymptotic stability is described. Our controlling procedure allows asymptotically unstable chaotic attractors to become practically ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2010
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-10-05061-0