3 research outputs found
Hidden attractors in fundamental problems and engineering models
Recently a concept of self-excited and hidden attractors was suggested: an
attractor is called a self-excited attractor if its basin of attraction
overlaps with neighborhood of an equilibrium, otherwise it is called a hidden
attractor. For example, hidden attractors are attractors in systems with no
equilibria or with only one stable equilibrium (a special case of
multistability and coexistence of attractors). While coexisting self-excited
attractors can be found using the standard computational procedure, there is no
standard way of predicting the existence or coexistence of hidden attractors in
a system. In this plenary survey lecture the concept of self-excited and hidden
attractors is discussed, and various corresponding examples of self-excited and
hidden attractors are considered
Minimal Length Scale Scenarios for Quantum Gravity
We review the question of whether the fundamental laws of nature limit our
ability to probe arbitrarily short distances. First, we examine what insights
can be gained from thought experiments for probes of shortest distances, and
summarize what can be learned from different approaches to a theory of quantum
gravity. Then we discuss some models that have been developed to implement a
minimal length scale in quantum mechanics and quantum field theory. These
models have entered the literature as the generalized uncertainty principle or
the modified dispersion relation, and have allowed the study of the effects of
a minimal length scale in quantum mechanics, quantum electrodynamics,
thermodynamics, black-hole physics and cosmology. Finally, we touch upon the
question of ways to circumvent the manifestation of a minimal length scale in
short-distance physics.Comment: Published version available at
http://www.livingreviews.org/lrr-2013-