Generalized exponential function and discrete growth models

Abstract

Here we show that a particular one-parameter generalization of the exponential function is suitable to unify most of the popular one-species discrete population dynamics models into a simple formula. A physical interpretation is given to this new introduced parameter in the context of the continuous Richards model, which remains valid for the discrete case. From the discretization of the continuous Richards' model (generalization of the Gompertz and Verhuslt models), one obtains a generalized logistic map and we briefly study its properties. Notice, however that the physical interpretation for the introduced parameter persists valid for the discrete case. Next, we generalize the (scramble competition) θ-Ricker discrete model and analytically calculate the fixed points as well as their stability. In contrast to previous generalizations, from the generalized θ-Ricker model one is able to retrieve either scramble or contest models.

Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

“…Differently from what was reported in Ref. [11], where the results have been obtained after 10 7 MC steps per spin, we have used 6.1 3 MC steps per spin, an equilibrium situation consistent with the one reported by Newman and Barkema [34]. This results in 1.5 × 10 6 -1.5 × 10 9 MC steps for the whole lattice of 16 2 up to 512 2 spins.…”

“…Many physicists believe that statistical mechanics generalizations with an extra parameter q [1] are suitable for studying the optimization combinatorial process, as, for example, simulated annealing (see, e.g., Refs. [2,3]) or areas such as econophysics [4,5], population dynamics and growth models [6][7][8][9], bibliometry [10], and others.…”

Nonlinear statistical coupling

“…We will show that the improved mathematical symmetry and direct modeling of a physical property provide advantages for the conceptual representation of stochastic systems impacted by sources of nonlinearity. Details of the translated q-calculus are described in [20] and has been utilized directly by Topsoe in [21], Martinez in [22], and Wang in [23] and as complementary analysis in for example [4,5]. The translation between Q and 1 Q − is equivalent to the multiplicative dual of q-statistics, which is…”

Sobre derivadas fracionárias

“…No final do século XX, já podemos mencionar estudos associados ao cálculo de ordem não inteira no Brasil, dentre eles além do Paraná [29], Santa Catarina [30] e Rio de Janeiro [31]. Aqui, a fim de mencionar o grupo de Lenzi, no Paraná, a partir desta data, selecionamos o artigo [32].…”