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) $\theta$-Ricker discrete model and analytically calculate the fixed points as well as their stability. In contrast to previous generalizations, from the generalized $\theta$-Ricker model one is able to retrieve either scramble or contest models.

7 pages, 6 figures and 2 tables

References in corpus (20)

• Statistical mechanics in the context of special relativity
• Non Linear Kinetics underlying Generalized Statistics
• Generalized Simulated Annealing
• Nonextensivity and multifractality in low-dimensional dissipative systems
• Statistical mechanics in the context of special relativity II
• A possible deformed algebra and calculus inspired in nonextensive thermostatistics
• Generalized algebra within a nonextensive statistics
• Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics
• Are citations of scientific papers a case of nonextensivity ?
• Power-Law Sensitivity to Initial Conditions within a Logistic-like Family of Maps: Fractality and Nonextensivity
• Convergence of the critical attractor of dissipative maps: Log-periodic oscillations, fractality and nonextensivity
• Convergence to the critical attractor of dissipative maps: Log-periodic oscillations, fractality and nonextensivity
• Thesaurus as a complex network
• Continuous growth models in terms of generalized logarithm and exponential functions
• Risk aversion in economic transactions
• Two-parameter generalization of the logarithm and exponential functions and Boltzmann-Gibbs-Shannon entropy
• Arithmetical and geometrical means of generalized logarithmic and exponential functions: generalized sum and product operators
• Algebra and calculus for Tsallis thermostatistics
• The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws
• Generalized Exponential Function and some of its Applications to Complex Systems

Cited by in corpus (15)

• Continuous growth models in terms of generalized logarithm and exponential functions
• Escort Evolutionary Game Theory
• Nonlinear statistical coupling
• Scaling Function, Universality and Analytical Solutions of Generalized One-Species Population Dynamics Models
• Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems
• Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model
• Fast, parallel and secure cryptography algorithm using Lorenz's attractor
• The additive property of the inconsistency degree in intertemporal decision making through the generalization of psychophysical laws
• Interplay between scales in the nonlocal FKPP equation
• Single-species fragmentation: the role of density-dependent feedbacks
• A risk profile for information fusion algorithms
• Full analytical solution and complete phase diagram analysis of the Verhulst-like two-species population dynamics model
• A generalized $q$ growth model based on nonadditive entropy
• Reduced Perplexity: A simplified perspective on assessing probabilistic forecasts
• Generalized Exponential Function and some of its Applications to Complex Systems