Chaotic sequences with eco-grammar systems

Grammar systems are abstract models of computation invented to formalize the agents systems of Artificial Intelligence. In this work we show a way to model dynamics able to represent chaotic sequences using Reproductive Simple Eco-grammars systems. Our system shows dynamics of population according to the logistic equation developed by May in 1973. We use an alphabet of symbols representing a population of “rabbit ” agents and “carrot ” resources. This work is going on the direction of approaching Artificial Intelligence, theoretical computer sciences and complex systems. 1. Eco-grammar systems Grammar systems [4,6,8,9,12,14] are recent abstract models of computation created to provide of a grammatical model of distributed processes. They are conceived as agent systems where each agent is a grammar. All the agents act concurrently to perform a derivation on a common sentential form that originally modeled blackboard architectures. The agents generate collectively a language. The objective of Grammar Systems is the study of agent systems from the point of view of the pure communication protocols. This approach looks for the increment of the generative power of grammars and for the decrement of the descriptive complexity. Notice that in Artificial Intelligence an agent system has various capabilities as perception, deliberation, reaction, communication and coordination, etc. which are not present in this proposal, that comes from Formal Language Theory. Eco-grammar systems [4] are a particular type of grammar systems created to model eco-systems. They are composed of an environment, a context free parallel rewriting system, or 0L system [12,15] together with a set of agents such that each agent has a set of context free rewriting rules called action rules. At each derivation step, agents act on the environmenta