Punctuated Evolution Due to Delayed Carrying Capacity

@inproceedings{Yukalov2009PunctuatedED,
  title={Punctuated Evolution Due to Delayed Carrying Capacity},
  author={Vyacheslav I. Yukalov and E. P. Yukalova and Didier Sornette},
  year={2009}
}
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42 Citations
Highly Influential Citations
5
Background Citations
19
Methods Citations
6

42 Citations

Population Dynamics with Nonlinear Delayed Carrying Capacity
TLDR
This work generalizes an exhaustive classification of the logistic equation where the carrying capacity is linearly dependent on the population with a time delay to the case of a nonlinear delayed carrying capacity, which changes the behavior of solutions to the evolution equation.
Dynamic Transition in Symbiotic Evolution Induced by Growth Rate Variation
TLDR
It is shown that, although the stationary states of the dynamical system do not depend on the growth rates, the latter influence the boundary of the basins of attraction, which explains this unusual effect of the qualitative change of dynamics by growth rate variation.
Multiple Equilibria and bifurcations in an Economic Growth Model with Endogenous Carrying Capacity
  • D. Cai
  • Economics
    Int. J. Bifurc. Chaos
  • 2010
TLDR
A model to analyze the structural change of an economic growth model with endogenous carrying capacity when the parameters vary is setup and it is proved that the dynamical system which describes the model has one, two or three equilibria under different conditions.
Extreme events in population dynamics with functional carrying capacity
TLDR
A class of models is introduced describing the evolution of population species whose carrying capacities are functionals of these populations, reflecting the fact that the correlations between populations can be realized not merely through direct interactions, but also through the influence of species on the carrying capacities of each other.
On the Dalgaard-Strulik Model with Logistic Population Growth Rate and Delayed-Carrying Capacity
Recently Dalgaard and Strulik have proposed (in Resour. Energy Econ. 33:782–797, 2011) an energy model of capital accumulation based on the mathematical framework developed by Solow-Swan and coupled…
Semi-analytical solution of a Generalized Delay Logistic Equation
In this master we show how to obtain a semi-analytical solution to the generalized delay logistic equation dx/dt = x(1 − x/(a + bx(t − τ)) via a method of steps. The results are supported by…
Modeling Symbiosis by Interactions Through Species Carrying Capacities
On the dynamics of the world demographic transition and financial-economic crises forecasts
The article considers dynamic processes involving non-linear power-law behavior in such apparently diverse spheres, as demographic dynamics and dynamics of prices of highly liquid commodities such as…
The analytical solutions of the harvesting Verhulst’s evolution equation
A cubic nonlinear population growth model for single species: theory, an explicit–implicit solution algorithm and applications
TLDR
This paper proposes a model based on a nonlinear cubic differential equation that reveals itself as a special subclass of Abel differential equations of first kind that violates the nonnegativity constraints on population sizes, and develops an explicit–implicit time-discrete numerical solution algorithm for this model.
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