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Let M be a compact Riemannian manifold. A self-interacting diffusion on M is a stochastic process solution to dX t = dW t (X t) − 1 t t 0 ∇V Xs (X t)ds dt where {W t } is a Brownian vector field on M and V x (y) = V (x, y) a smooth function. Let µ t = 1 t t 0 δ Xs ds denote the normalized occupation measure of X t. We prove that, when V is symmetric, µ t(More)
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a r t i c l e i n f o a b s t r a c t Attractors of cooperative dynamical systems are particularly simple; for example, a nontrivial periodic orbit cannot be an attractor, and orbits are nowhere dense. This paper provides characterizations of attractors for the wider class of coherent systems, defined by the property that all directed feedback loops are(More)