scholarly journals Chaos in a single-species discrete population model with stage structure and birth pulses

2014 ◽  
Vol 2014 (1) ◽  
Author(s):  
Hui Fang
Keyword(s):  
Population Model ◽  
Stage Structure ◽  
Single Species ◽  
Discrete Population ◽  
Discrete Population Model

THE EFFECT OF SEASONAL HARVESTING ON A STAGE-STRUCTURED DISCRETE MODEL WITH BIRTH PULSES

2006 ◽  
Vol 16 (09) ◽  
pp. 2575-2586 ◽  
Author(s):  
SHUJING GAO ◽  
LANSUN CHEN
Keyword(s):  
Single Pulse ◽  
Stage Structure ◽  
Single Species ◽  
Fish Population ◽  
Basins Of Attraction ◽  
Fish Stock ◽  
Strong Impact ◽  
Natural Period ◽  
Discrete Population ◽  
Mature Fish

In this paper, we propose an exploited single-species discrete population model with stage structure for the dynamics in a fish population for which births occur in a single pulse once per time period. Using the stroboscopic map, we obtain an exact cycle of the system, and obtain the threshold conditions for its stability. Bifurcation diagrams are constructed with the birth rate (or harvesting effort) as the bifurcation parameter, and these are observed to display complex dynamic behaviors, including chaotic bands with period windows, pitchfork and tangent bifurcation, nonunique dynamics (meaning that several attractors or attractor and chaos coexist), basins of attraction and attractor crisis. This suggests that birth pulse provides a natural period or cyclicity that makes the dynamical behaviors more complex. Moreover, we show that the timing of harvesting has a strong impact on the persistence of the fish population, on the volume of mature fish stock and on the maximum annual-sustainable yield. An interesting result is obtained that, after the birth pulses, the population can sustain much higher harvesting effort if the mature fish is removed as early in the season as possible.

scholarly journals Stability analysis of stochastic Ricker population model

2006 ◽  
Vol 2006 ◽  
pp. 1-13 ◽  
Author(s):  
Natali Hritonenko ◽  
Alexandra Rodkina ◽  
Yuri Yatsenko
Keyword(s):  
Stability Analysis ◽  
Population Model ◽  
Noise Intensity ◽  
Reproduction Rate ◽  
Stochastic Noise ◽  
Population Extinction ◽  
Discrete Population ◽  
Noise Impacts ◽  
Discrete Population Model

A stochastic generalization of the Ricker discrete population model is studied under the assumption that noise impacts the population reproduction rate. The obtained results demonstrate that the demographic-type stochastic noise increases the risk of the population extinction. In particular, the paper establishes conditions on the noise intensity under which the population will extinct even if the corresponding population with no noise survives.

GLOBAL STABILITY OF A NONLINEAR DISCRETE POPULATION MODEL WITH TIME DELAYS

2007 ◽  
Vol 10 (03) ◽  
pp. 315-333
Author(s):  
NA FANG ◽  
XIAOXING CHEN
Keyword(s):  
Global Stability ◽  
Positive Solution ◽  
Positive Solutions ◽  
Population Model ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Volterra Type ◽  
Discrete Population ◽  
Liapunov Functionals ◽  
Discrete Population Model

The global stability of a nonlinear discrete population model of Volterra type is studied. The model incorporates time delays. By linearization of the model at positive solutions and construction of Liapunov functionals, sufficient conditions are obtained to ensure that a positive solution of the model is stable and attracts all positive solutions. An example shows the feasibility of our main results.

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