Scaling Function, Universality and Analytical Solutions of Generalized One-Species Population Dynamics Models
arXiv:1010.2950 · doi:10.1103/PhysRevE.83.061902
Abstract
We consider several one-species population dynamics model with finite and infinite carrying capacity, time dependent growth and effort rates and solve them analytically. We show that defining suitable scaling functions for a given time, one is able to demonstrate that their ratio with respect to its initial value is universal. This ratio is independent from the initial condition and from the model parameters. Although the effort rate does not break the model universality it produces a transition between the species extinction and survival. A general formula is furnished to obtain the scaling functions.
8 pages and 4 figures
References in corpus (7)
- Correlated noise in a logistic growth model
- Verhulst model with Levy white noise excitation
- Continuous growth models in terms of generalized logarithm and exponential functions
- Generalized exponential function and discrete growth models
- Arithmetical and geometrical means of generalized logarithmic and exponential functions: generalized sum and product operators
- An exact analytical solution for generalized growth models driven by a Markovian dichotomic noise
- Cancer and nonextensive statistics
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