THE EFFECT OF IMPULSIVE SPRAYING PESTICIDE ON STAGE-STRUCTURED POPULATION MODELS WITH BIRTH PULSE

2005 ◽  
Vol 13 (01) ◽  
pp. 31-44 ◽  
Author(s):  
BING LIU ◽  
ZHIDONG TENG ◽  
LANSUN CHEN
Keyword(s):  
Discrete Dynamical System ◽  
Period Doubling ◽  
Fixed Time ◽  
Population Models ◽  
Strong Impact ◽  
Structured Population Models ◽  
Birth Pulse ◽  
Structured Population ◽  
Dynamical Behaviors ◽  
Threshold Conditions

In most models of population dynamics, increases in population due to birth are assumed to be time dependent, but many species reproduce only a single period of the year. In this paper, we construct a stage-structured pest model with birth pulse and periodic spraying pesticide at fixed time in each birth period by using impulsive differential equation. Using the discrete dynamical system determined by the stroboscopic map, we obtain an exact periodic solution of systems which are with Ricker function or Beverton-Holt function, and obtain the threshold conditions for their stability. Further, we show that the time of spraying pesticide has a strong impact on the number of the mature pest population. Our results imply that the best time of spraying pesticide is at the end of the season, that is before and near the time of birth. Finally, by numerical simulations we find that the dynamical behaviors of the stage-structured population models with birth pulse and impulsive spraying pesticide are very complex, including period-doubling cascade, period-halving cascade, chaotic bands with periodic windows and "period-adding" phenomena.

DYNAMIC COMPLEXITIES IN AN EPIDEMIC MODEL WITH BIRTH PULSES AND PULSE CULLING

2007 ◽  
Vol 17 (02) ◽  
pp. 521-533 ◽  
Author(s):  
SHUJING GAO ◽  
LANSUN CHEN ◽  
ZHIDONG TENG ◽  
DEHUI XIE
Keyword(s):  
Birth Rate ◽  
Discrete Dynamical System ◽  
Sufficient Conditions ◽  
Period Doubling ◽  
Basins Of Attraction ◽  
Complex Dynamic ◽  
Natural Period ◽  
Dynamical Behaviors ◽  
Threshold Conditions ◽  
Fixed Times

In this paper, we propose a model for the dynamics of a fatal infectious disease in a wild animal population with birth pulses and pulse culling, where periodic birth pulses and pulse culling occur at different fixed times. Using the discrete dynamical system determined by 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 culling effort) as the bifurcation parameter, and these are observed to display complex dynamic behaviors, including chaotic bands with period windows, period-doubling and period-halving bifurcations, pitch-fork and tangent bifurcations, nonunique dynamics (meaning that several attractors or attractor and chaos coexist), basins of attraction and attractor crisis. This suggests that birth pulses and pulse culling provide a natural period or cyclicity that makes the dynamical behaviors more complex. Moreover, we investigate the sufficient conditions for global stability of semi-trivial periodic solutions.

scholarly journals On the formulation and analysis of general deterministic structured population models

2001 ◽  
Vol 43 (2) ◽  
pp. 157-189 ◽  
Author(s):  
O. Diekmann ◽  
M. Gyllenberg ◽  
H. Huang ◽  
M. Kirkilionis ◽  
J.A.J. Metz ◽  
...  
Keyword(s):  
Population Models ◽  
Structured Population Models ◽  
Structured Population

scholarly journals Splitting-particle methods for structured population models: Convergence and applications

2014 ◽  
Vol 24 (11) ◽  
pp. 2171-2197 ◽  
Author(s):  
J. A. Carrillo ◽  
P. Gwiazda ◽  
A. Ulikowska
Keyword(s):  
Numerical Scheme ◽  
Order Of Convergence ◽  
Operator Splitting ◽  
Population Models ◽  
Particle Simulation ◽  
Particle Methods ◽  
Test Cases ◽  
Structured Population Models ◽  
Convergence Error ◽  
Structured Population

We propose a new numerical scheme designed for a wide class of structured population models based on the idea of operator splitting and particle approximations. This scheme is related to the Escalator Boxcar Train (EBT) method commonly used in biology, which is in essence an analogue of particle methods used in physics. Our method exploits the split-up technique, thanks to which the transport step and the nonlocal integral terms in the equation can be separately considered. The order of convergence of the proposed method is obtained in the natural space of finite non-negative Radon measures equipped with the flat metric. This convergence is studied even adding reconstruction and approximation steps in the particle simulation to keep the number of approximation particles under control. We validate our scheme in several test cases showing the theoretical convergence error. Finally, we use the scheme in situations in which the EBT method does not apply showing the flexibility of this new method to cope with the different terms in general structured population models.

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