Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model

P.S. Mandal; M. Banerjee

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 3, page 99-116
  • ISSN: 0973-5348

Abstract

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An eco-epidemiological model of susceptible Tilapia fish, infected Tilapia fish and Pelicans is investigated by several author based upon the work initiated by Chattopadhyay and Bairagi (Ecol. Model., 136, 103–112, 2001). In this paper, we investigate the dynamics of the same model by considering different parameters involved with the model as bifurcation parameters in details. Considering the intrinsic growth rate of susceptible Tilapia fish as bifurcation parameter, we demonstrate the period doubling route to chaos. Next we consider the force of infection as bifurcation parameter and demonstrate the occurrence of two successive Hopf-bifurcations. We identify the existence of backward Hopf-bifurcation when the death rate of predators is considered as bifurcation parameter. Finally we construct a stochastic differential equation model corresponding to the deterministic model to understand the role of demographic stochasticity. Exhaustive numerical simulation of the stochastic model reveals the large amplitude fluctuation in the population of fish and Pelicans for certain parameter values. Extinction scenario for Pelicans is also captured from the stochastic model.

How to cite

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Mandal, P.S., and Banerjee, M.. "Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model." Mathematical Modelling of Natural Phenomena 7.3 (2012): 99-116. <http://eudml.org/doc/222371>.

@article{Mandal2012,
abstract = {An eco-epidemiological model of susceptible Tilapia fish, infected Tilapia fish and Pelicans is investigated by several author based upon the work initiated by Chattopadhyay and Bairagi (Ecol. Model., 136, 103–112, 2001). In this paper, we investigate the dynamics of the same model by considering different parameters involved with the model as bifurcation parameters in details. Considering the intrinsic growth rate of susceptible Tilapia fish as bifurcation parameter, we demonstrate the period doubling route to chaos. Next we consider the force of infection as bifurcation parameter and demonstrate the occurrence of two successive Hopf-bifurcations. We identify the existence of backward Hopf-bifurcation when the death rate of predators is considered as bifurcation parameter. Finally we construct a stochastic differential equation model corresponding to the deterministic model to understand the role of demographic stochasticity. Exhaustive numerical simulation of the stochastic model reveals the large amplitude fluctuation in the population of fish and Pelicans for certain parameter values. Extinction scenario for Pelicans is also captured from the stochastic model.},
author = {Mandal, P.S., Banerjee, M.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {Eco-epidemiology; stability; Hopf-bifurcation; chaos; stochasticity; extinction; eco-epidemiology},
language = {eng},
month = {6},
number = {3},
pages = {99-116},
publisher = {EDP Sciences},
title = {Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model},
url = {http://eudml.org/doc/222371},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Mandal, P.S.
AU - Banerjee, M.
TI - Deterministic Chaos vs. Stochastic Fluctuation in an Eco-epidemic Model
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/6//
PB - EDP Sciences
VL - 7
IS - 3
SP - 99
EP - 116
AB - An eco-epidemiological model of susceptible Tilapia fish, infected Tilapia fish and Pelicans is investigated by several author based upon the work initiated by Chattopadhyay and Bairagi (Ecol. Model., 136, 103–112, 2001). In this paper, we investigate the dynamics of the same model by considering different parameters involved with the model as bifurcation parameters in details. Considering the intrinsic growth rate of susceptible Tilapia fish as bifurcation parameter, we demonstrate the period doubling route to chaos. Next we consider the force of infection as bifurcation parameter and demonstrate the occurrence of two successive Hopf-bifurcations. We identify the existence of backward Hopf-bifurcation when the death rate of predators is considered as bifurcation parameter. Finally we construct a stochastic differential equation model corresponding to the deterministic model to understand the role of demographic stochasticity. Exhaustive numerical simulation of the stochastic model reveals the large amplitude fluctuation in the population of fish and Pelicans for certain parameter values. Extinction scenario for Pelicans is also captured from the stochastic model.
LA - eng
KW - Eco-epidemiology; stability; Hopf-bifurcation; chaos; stochasticity; extinction; eco-epidemiology
UR - http://eudml.org/doc/222371
ER -

References

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