Periodic attractors of random truncator maps
arXiv:math/0606667 · doi:10.1016/j.physa.2007.02.090
Abstract
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.
8 pages, presented at APFA5
References in corpus (12)
- Genetic networks with canalyzing Boolean rules are always stable
- Scaling in ordered and critical random Boolean networks
- Iterated function systems, Ruelle operators, and invariant projective measures
- Dynamics of price and trading volume in a spin model of stock markets with heterogeneous agents
- On the number of attractors in random Boolean networks
- Martingales, endomorphisms, and covariant systems of operators in Hilbert space
- Uncertainty relations in models of market microstructure
- Random maps and attractors in random Boolean networks
- Statistical properties of the phase transitions in a spin model for market microstructure
- Properties of a renewal process approximation for a spin market model
- The Number of Attractors in Kauffman Networks
- Counting attractors in synchronously updated random Boolean networks