Chebanov law and Vakar formula in mathematical models of complex systems

Abstract

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; c) 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.

Behavior of pyrophite shrubs in mediterranean terrestrial ecosystems (i): Population and reproductive model

“…The MARIOLA model (Mateu, Usó and Montes, 1998;Usó-Domènech, Villacampa, Stübing, Karjalainen and Ramo, 1995;Usó-Domènech, Mateu and Lopez, 2000; Usó-Doménech, Nescolarde-Selva, Lloret-Climent and Meng, 2016. ), so called for having taken as the base the mountainous terrestrial ecosystem of the Sierra de Mariola (Alicante, Spain), is a dynamic model based on System Dynamics (Forrester, 1961), in which differential equations (state equations) are set up hypothetically, and flow variables are obtained from field observations using multiple regression equations (Cortés, Villacampa, Mateu and Usó-Doménech, 2000; Nescolarde-Selva, Usó-Doménech, Lloret-Climent,. and González-Franco, 2015;Lopez, 1997, 2000;Usó-Doménech, Nescolarde-Selva, Lloret-Climent and Meng, 2016).…”

A dialectical vision of mathematical models of complex systems

“…For deductive-inductive modelling process (Nescolarde-Selva et al , 2015b; Nescolarde-Selva et al , 2016b; Usó-Domènech et al , 1997; Usó-Domènech and Villacampa, 2001; Usó-Domènech et al , 2001; Usó-Domènech and Sastre-Vazquez, 2002; Usó-Domènech and Mateu, 2004; Usó-Domènech et al , 2006a, 2006b; Usó-Domènech et al , 2016a, 2016b, 2016c; Villacampa and Usó-Domènech, 1999; Villacampa et al , 1999) the authors use the following assumptions to deal with complex reality: The construction of a causal model based on previous theories of the reality to study. In term, it can be divided into the following phases: Choose relevant objects or variables related to the proposed objectives.…”