This article tries to give a general vision of the mathematical methods used to model biological processes. There are two kinds of methods: deterministics using dynamical systems theory and probabilistics, using stochastic differential equations. However, three points can not be neglected for biological processes: complexity, unpredictability and diversity of time scales.Este trabalho trata de uma visão panorâmica dos principais métodos utilizados, atualmente, na modelagem matemática de processos biológicos. Esses métodos são muito variados, com enfoques que, às vezes, são determinísticos, utilizando (...) a teoria dos sistemas dinâmicos e, às vezes, são probabilísticos, lançando mão das equações diferenciais estocásticas. Em todos eles, entretanto, três fatores inerentes aos processos biológicos não podem deixar de ser considerados: a complexidade, a imprevisibilidade e a diversidade de escalas temporais. (shrink)

This work is a generalization of the López-Ruiz, Mancini, and Calbet (LMC) and Shiner, Davison, and Landsberg (SDL) complexity measures, considering that the state of a system or process is represented by a continuous temporal series of a dynamical variable. As the two complexity measures are based on the calculation of informational entropy, an equivalent information source is defined by using partitions of the dynamical variable range. During the time intervals, the information associated with the measured dynamical variable is the (...) seed to calculate instantaneous LMC and SDL measures. To show how the methodology works generating indicators, two examples, one concerning meteorological data and the other concerning economic data, are presented and discussed. (shrink)

Some concepts related to the utilization of Dynamical Systems Theory on complex systems problems are presented. Using these concepts, we suggest that two dynamics can be established: a short-term one and a long-term one, and both of them are connected to the system's organization processes.Foram apresentados alguns conceitos relativos à utilização da Teoria dos Sistemas Dinâmicos em problemas de sistemas complexos. A apresentação destes conceitos centra-se no estabelecimento de duas dinâmicas: uma de curto termo e outra de longo termo, relacionando-as (...) com os processos de organização dos sistemas. (shrink)

This work presents a discussion about the application of the Kolmogorov; López-Ruiz, Mancini, and Calbet ; and Shiner, Davison, and Landsberg complexity measures to a common situation in physics described by the Maxwell–Boltzmann distribution. The first idea about complexity measure started in computer science and was proposed by Kolmogorov, calculated similarly to the informational entropy. Kolmogorov measure when applied to natural phenomena, presents higher values associated with disorder and lower to order. However, it is considered that high complexity must be (...) associated to intermediate states between order and disorder. Consequently, LMC and SDL measures were defined and used in attempts to model natural phenomena but with the inconvenience of being defined for discrete probability distributions defined over finite intervals. Here, adapting the definitions to a continuous variable, the three measures are applied to the known Maxwell–Boltzmann distribution describing thermal neutron velocity in a power reactor, allowing extension of complexity measures to a continuous physical situation and giving possible discussions about the phenomenon. (shrink)