The aim of this paper is to provide a brief review of the main results in the theory of discrete-time monotone dynamics.
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)
In this paper we report on some new architectures for neural computation, motivated in part by biological considerations. One of our goals is to demonstrate that it is just as easy for a neural net to compute with arbitrary attractors--oscillatory or chaotic--as with the more usual asymptotically stable fixed points. The advantages (if any) of such… (More)
Fudenberg and Kreps (1993) consider adaptive learning processes, in the spirit of ctitious play, for innnitely repeated games of incomplete information having randomly perturbed payoos. They proved the convergence of the adaptive process for 22 games with a unique completely mixed Nash equilibrium. Kaniovski and Young (1995) proved the convergence of the… (More)
Certain dynamical models of competition are shown to have a unique invariant hypersurface Σ, having simple geometry and topology, such that every non-zero tractory is asymptotic to a trajectory in Σ.
\Real" and \ghost" bifurcation dynamics in diierence schemes for ODEs, in Numerical Methods for Bifurcation Problems (T. Discrete-time versus continuous-time neural networks, J. Comput.
article info abstract Article history: 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 o fa t t r a c t o r sf o rt h ew i d e rc l a s so fcoherent systems, defined by the property that all directed… (More)