44 Citations
Population Dynamics with Nonlinear Delayed Carrying Capacity
- MathematicsInt. J. Bifurc. Chaos
- 2014
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
- EconomicsInt. J. Bifurc. Chaos
- 2017
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
- EconomicsInt. J. Bifurc. Chaos
- 2010
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
- Mathematics
- 2012
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
- Economics
- 2013
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
- Mathematics
- 2010
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…
On the dynamics of the world demographic transition and financial-economic crises forecasts
- Economics
- 2012
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…
Utility Rate Equations of Group Population Dynamics in Biological and Social Systems
- EconomicsPloS one
- 2013
It is found that, in a self-organized society, neither defectors nor regulators can overpass the maximal fractions of about each and, in agreement with the data for bee and ant colonies, the classification of societies by their distance from equilibrium is proposed.
References
SHOWING 1-10 OF 87 REFERENCES
An alternative formulation for a delayed logistic equation.
- MathematicsJournal of theoretical biology
- 2006
Solution multistability in first-order nonlinear differential delay equations.
- MathematicsChaos
- 1993
The dependence of solution behavior to perturbations of the initial function (IF) in a class of nonlinear differential delay equations (DDEs) is investigated. The structure of basins of attraction of…
Stability of some test equations with delay
- Mathematics
- 1994
The authors propose some techniques to obtain stability conditions for certain differential equations with delay. These techniques are applied to three concrete test situations. In the first and…
Finite-time singularity in the dynamics of the world population, economic and financial indices
- Economics
- 2001
On computing the maximal delay intervals for stability of linear delay systems
- MathematicsProceedings of 1994 American Control Conference - ACC '94
- 1994
This paper is concerned with stability properties of linear time-invariant delay systems. The author considers both retarded and neutral delay systems expressed in state space form. The author's main…
Stability and Oscillations in Delay Differential Equations of Population Dynamics
- Mathematics
- 1992
1. The Delay Logistic Equation. 2. Delay Induced Bifurcation to Periodicity. 3. Methods of Linear Analysis. 4. Global Attractivity. 5. Models of Neutral Differential Systems. References. Index.