Global dynamics in a stage-structured discrete-time population model with harvesting

2012 ◽  
Vol 297 ◽  
pp. 148-165 ◽  
Author(s):  
Eduardo Liz ◽  
Paweł Pilarczyk
Keyword(s):  
Discrete Time ◽  
Population Model ◽  
Global Dynamics

scholarly journals Predicting the spatio-temporal distribution of Culicoides imicola in Sardinia using a discrete-time population model

2012 ◽  
Vol 5 (1) ◽  
Author(s):  
Thibaud Rigot ◽  
Annamaria Conte ◽  
Maria Goffredo ◽  
Els Ducheyne ◽  
Guy Hendrickx ◽  
...  
Keyword(s):  
Discrete Time ◽  
Population Model ◽  
Temporal Distribution ◽  
Culicoides Imicola ◽  
Spatio Temporal

scholarly journals Local and Global Dynamics in a Discrete Time Growth Model with Nonconcave Production Function

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Serena Brianzoni ◽  
Cristiana Mammana ◽  
Elisabetta Michetti
Keyword(s):  
Production Function ◽  
Growth Model ◽  
Discrete Time ◽  
Production Functions ◽  
Elasticity Of Substitution ◽  
Global Dynamics ◽  
Production Factors ◽  
Local And Global Dynamics ◽  
Complex Features

We study the dynamics shown by the discrete time neoclassical one-sector growth model with differential savings while assuming a nonconcave production function. We prove that complex features exhibited are related both to the structure of the coexixting attractors and to their basins. We also show that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, confirming the results obtained while considering concave production functions.

A DARWINIAN DYNAMIC MODEL FOR THE EVOLUTION OF POST-REPRODUCTION SURVIVAL

2021 ◽  
pp. 1-18
Author(s):  
J. M. CUSHING ◽  
KATHRYN STEFANKO
Keyword(s):  
Natural Selection ◽  
Dynamic Model ◽  
Discrete Time ◽  
Population Model ◽  
Bifurcation Theory ◽  
Allee Effect ◽  
Phenotypic Trait ◽  
Trade Off ◽  
The Stability ◽  
Low Dimensional

We derive and study a Darwinian dynamic model based on a low-dimensional discrete- time population model focused on two features: density-dependent fertility and a trade-off between inherent (density free) fertility and post-reproduction survival. Both features are assumed to be dependent on a phenotypic trait subject to natural selection. The model tracks the dynamics of the population coupled with that of the population mean trait. We study the stability properties of equilibria by means of bifurcation theory. Whether post-reproduction survival at equilibrium is low or high is shown, in this model, to depend significantly on the nature of the trait dependence of the density effects. An Allee effect can also play a significant role.

Bifurcations and chaos control in a discrete-time biological model

2020 ◽  
Vol 13 (04) ◽  
pp. 2050022 ◽  
Author(s):  
A. Q. Khan ◽  
T. Khalique
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Control Method ◽  
Complex Dynamics ◽  
Small Neighborhood ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Flip Bifurcation ◽  
Time Model ◽  
Predator Prey Model

In this paper, bifurcations and chaos control in a discrete-time Lotka–Volterra predator–prey model have been studied in quadrant-[Formula: see text]. It is shown that for all parametric values, model has boundary equilibria: [Formula: see text], and the unique positive equilibrium point: [Formula: see text] if [Formula: see text]. By Linearization method, we explored the local dynamics along with different topological classifications about equilibria. We also explored the boundedness of positive solution, global dynamics, and existence of prime-period and periodic points of the model. It is explored that flip bifurcation occurs about boundary equilibria: [Formula: see text], and also there exists a flip bifurcation when parameters of the discrete-time model vary in a small neighborhood of [Formula: see text]. Further, it is also explored that about [Formula: see text] the model undergoes a N–S bifurcation, and meanwhile a stable close invariant curves appears. From the perspective of biology, these curves imply that between predator and prey populations, there exist periodic or quasi-periodic oscillations. Some simulations are presented to illustrate not only main results but also reveals the complex dynamics such as the orbits of period-2,3,13,15,17 and 23. The Maximum Lyapunov exponents as well as fractal dimension are computed numerically to justify the chaotic behaviors in the model. Finally, feedback control method is applied to stabilize chaos existing in the model.

Impact of Dispersion on Dynamics of a Discrete Metapopulation Model

2007 ◽  
Vol 14 (04) ◽  
pp. 379-396 ◽  
Author(s):  
Yu Huang ◽  
Xingfu Zou
Keyword(s):  
Periodic Orbit ◽  
Discrete Time ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Metapopulation Model ◽  
Time Model ◽  
Discrete Time Model ◽  
Global Extinction ◽  
Dispersion Terms ◽  
The Impact

We propose and analyze a discrete time model for metapopulation on two patches with local logistic dynamics. The model carries a delay in the dispersion terms, and our results on this model show that the impact of the dispersion on the global dynamics of the metapopulation is complicated and interesting: it can affect the existence of a positive equilibrium; it can either drive the metapopulation to global extinction, or prevent the metapopulation from going to global extinction and stabilize a positive equilibrium; it can also destabilize a positive equilibrium or a periodic orbit.

A note on a population model for breeding colonies

1983 ◽  
Vol 36 (3) ◽  
pp. 489-492
Author(s):  
H. Kushner ◽  
E. T. Angelakos
Keyword(s):  
Population Size ◽  
Discrete Time ◽  
Colony Size ◽  
Population Model ◽  
Optimization Problem ◽  
Reproductive Rate ◽  
Breeding Colony ◽  
Net Reproductive Rate ◽  
Applied Model ◽  
Green Monkeys

ABSTRACTA discrete-time population model is presented which is specific to the characteristics of a breeding colony. It is intended to be a rigorous yet an easily applied model. The model is based on a female-dominated demographic system with constraints on colony size. Fecundity and survival probabilities are incorporated into a net reproductive rate which is age-specific and time and population size invariant. The model is applied to solve an optimization problem for a breeding colony of African Green monkeys and to examine a set of external constraints imposed on the colony.

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