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This book gathers papers from the International Conference on
Differential & Difference Equations and Applications 2017
(ICDDEA 2017), held in Lisbon, Portugal on June 5-9, 2017. The
editors have compiled the strongest research presented at the
conference, providing readers with valuable insights into new
trends in the field, as well as applications and high-level survey
results. The goal of the ICDDEA was to promote fruitful
collaborations between researchers in the fields of differential
and difference equations. All areas of differential and difference
equations are represented, with a special emphasis on applications.
This book offers an introduction to the theory of non-autonomous
and stochastic dynamical systems, with a focus on the importance of
the theory in the Applied Sciences. It starts by discussing the
basic concepts from the theory of autonomous dynamical systems,
which are easier to understand and can be used as the motivation
for the non-autonomous and stochastic situations. The book
subsequently establishes a framework for non-autonomous dynamical
systems, and in particular describes the various approaches
currently available for analysing the long-term behaviour of
non-autonomous problems. Here, the major focus is on the novel
theory of pullback attractors, which is still under development. In
turn, the third part represents the main body of the book,
introducing the theory of random dynamical systems and random
attractors and revealing how it may be a suitable candidate for
handling realistic models with stochasticity. A discussion of
future research directions serves to round out the coverage.
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