We formulate stochastic robust optimal control problems, motivated by applications arising in interconnected economic systems, or spatially extended economies. We study in detail linear quadratic problems and nonlinear problems. We derive optimal robust controls and identify conditions under...

We present methods and tools that can be used to study dynamic environmental resource management in a spatial setting, to explore spatially dependent regulation, and to understand pattern formation. In particular, we present the maximum principle and its use in the context of the emerging...

A unified approach is proposed, which integrates game-theoretical models with models of directed motion. Specifically, strategic interactions in space and imitation of more successful neighboring strategies, as studied by spatial games, are combined with success-driven migration based on "test...

This paper reviews recent progress in modeling collective behaviors in myxobacteria using lattice gas cellular automata approach (LGCA). Myxobacteria are social bacteria that swarm, glide on surfaces and feed cooperatively. When starved, tens of thousands of cells change their movement pattern...

We observe a marked increase in the spatial homogeneity of the popularity of first names across the United States in recent decades. We explain this by calibrating a modified standard model of neutral cultural evolution to the record of first name popularities for the United States as a whole...

Spatial evolutionary games model individuals who are distributed in a spa- tial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic ap- proximations of the microscopic updating stochastic processes....

We consider a reaction-diffusion system in crossed electric and magnetic fields lying on the reaction plane. It is shown that a charge separation along the direction normal to the reaction plane resulting in a diffusional flux may cause a differential flow induced chemical instability and...

We study the propagation of periodic pulse trains in excitable media exposed to external spatio-temporal noise using the light-sensitive Belousov-Zhabotinsky reaction with the underlying Oregonator model as representative example. In the weak noise approximation we find noise-induced transitions...