Punctuated Evolution Due to Delayed Carrying Capacity

  title={Punctuated Evolution Due to Delayed Carrying Capacity},
  author={Vyacheslav I. Yukalov and E. P. Yukalova and Didier Sornette},

Population Dynamics with Nonlinear Delayed Carrying Capacity

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

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
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

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

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

Utility Rate Equations of Group Population Dynamics in Biological and Social Systems

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.



Solution multistability in first-order nonlinear differential delay equations.

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

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

On computing the maximal delay intervals for stability of linear delay systems

  • Jie Chen
  • Mathematics
    Proceedings 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

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.