Introduction to Coding Theory for Flow Equations of Complex Systems Models

The modeling of complex dynamic systems depends on the solution of a differential equations system. Some problems appear because we do not know the mathematical expressions of the said equations. Enough numerical data of the system variables are known. The authors, think that it is very important to establish a code between the different languages to let them codify and decodify information. Coding permits us to reduce the study of some objects to others. Mathematical expressions are used to model certain variables of the system are complex, so it is convenient to define an alphabet code determining the correspondence between these equations and words in the alphabet. In this paper the authors begin with the introduction to the coding and decoding of complex structural systems modeling.

Syntactic and Semantic Relationships in Models of Complex Systems: An Ecological Case

In this paper, the authors extend and generalize the methodology based on the dynamics of systems with the use of differential equations as equations of state, allowing that first order transformed functions not only apply to the primitive or original variables, but also doing so to more complex expressions derived from them, and extending the rules that determine the generation of transformed superior to zero order (variable or primitive). Also, it is demonstrated that for all models of complex reality, there exists a complex model from the syntactic and semantic point of view. The theory is exemplified with a concrete model: MARIOLA model.

An Ecological Model for Predicting Behaviour of Mediterranean Shrublands

In order to build dynamic models for prediction and management of degraded Mediterranean forest areas was necessary to build MARIOLA model, which is a calculation computer program. This model includes the following subprograms. 1) bioshrub program, which calculates total, green and woody shrubs biomass and it establishes the time differences to calculate the growth. 2) selego program, which builds the flow equations from the experimental data. It is based on advanced procedures of statistical multiple regression. 3) VEGETATION program, which solves the state equations with Euler or Runge-Kutta integration methods. Each one of these subprograms can act as independent or as linked programs.

Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.