Leading indicators of critical transitions: theory or practice?

Vasilis Dakos, Egbert van Nes, and Marten Scheffer summarize their recent results published in Nature on early-warning signals for critical transitions in a variety of systems ranging from fisheries to climate to financial markets.

Why Do Math

Inspired by the frequent need to answer the question, Why Do Math is a SIAM-sponsored website highlighting many of the exciting contributions made by computational science and mathematics to science, society, and everyday life. Though not specifically about dynamical systems, it includes many dynamical systems related topics (several of which are linked in the DSWeb Tutorials Section). The website is currently under development, but a number of tutorials are already available for view, on The America's Cup, Coclear Implants, Mathematics of Neuroscience, Space Travel, Tomography, Voting, and Wavelets.

Finding Appropriate Dynamics for the Social Sciences

The growing area of "mathematical social sciences" has provided valued insights for several disciplines, but a key aspect of this development desperately needs help from mathematicians who are skilled in dynamical systems. Namely, although "change" obviously is a central feature for all of the social sciences, it is not clear how it should be modeled. Indeed, in a real sense, this article is a call for help; it is an appeal for more people from the dynamical systems community to become involved. What makes the challenge attractive is that, once the appropriate dynamics are discovered, they most surely will involve features that differ from what we currently see in the literature. To introduce what causes some of the complexities of these areas, results and difficulties associated with price dynamics are described. As it will become clear, much less is known about how prices change than the reader might have expected.

The cat's cradle, stirring, and topological complexity

There are several physical situations in which the tangling of a loop is relevant: the game of cat's cradle is a simple example, but a more important application involves the stirring of a fluid by rods. Here we discuss how elementary topology constrains the types of mappings that can occur on a surface, for example when the surface is the domain of a two-dimensional fluid.

Two jobs, two countries, two homes

Yulij Il’yashenko is well known in the dynamical systems community for his work on the 16th Hilbert problem, generic properties of dynamical systems, and non-local bifurcations. He works part-time both at Cornell University in the USA and at Moscow State University, the Independent University and the Steklov Institute in Russia. Hinke Osinga asked him what it was like to grow up in the former USSR and how he has come to enjoy his life split between two continents.