516 research outputs found
Periodic attractors of random truncator maps
This paper introduces the \textit{truncator} map as a dynamical system on the
space of configurations of an interacting particle system. We represent the
symbolic dynamics generated by this system as a non-commutative algebra and
classify its periodic orbits using properties of endomorphisms of the resulting
algebraic structure. A stochastic model is constructed on these endomorphisms,
which leads to the classification of the distribution of periodic orbits for
random truncator maps. This framework is applied to investigate the periodic
transitions of Bornholdt's spin market model.Comment: 8 pages, presented at APFA
Hierarchical Economic Agents and their Interactions
We present a new type of spin market model, populated by hierarchical agents,
represented as configurations of sites and arcs in an evolving network. We
describe two analytic techniques for investigating the asymptotic behavior of
this model: one based on the spectral theory of Markov chains and another
exploiting contingent submartingales to construct a deterministic cellular
automaton that approximates the stochastic dynamics. Our study of this system
documents a phase transition between a sub-critical and a super-critical regime
based on the values of a coupling constant that modulates the tradeoff between
local majority and global minority forces. In conclusion, we offer a
speculative socioeconomic interpretation of the resulting distributional
properties of the system.Comment: 38 pages, 13 figures, presented at the 2013 WEHIA conference; to
appear in Journal of Economic Interaction and Coordination, to appear in
Journal of Economic Interaction and Coordinatio
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