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Does theta-logistic growth have any stabilizing effect on population dynamics? A study on the Salton Sea ecology. (English) Zbl 1433.92069

Summary: The Salton Sea, located in the south-east desert of California, is now turning out to be a harmful environment for both the fish population as well as the traveler birds mainly due to the sufficient salinity of sea water for which the susceptible preys are being infected. J. Chattopadhyay, P. D. N. Srinivasu and N. Bairagi [“Pelicans at risk in Salton Sea – an eco-epidemiological model. II”, Ecol. Model. 167, 199 (2003)] proposed and analyzed an eco-epidemiological model of Salton Sea. In the present paper, we propose a more realistic discrete time extension of their three component continuous model, consisting of susceptible fish population, infected fish population and their predator (the pelican population). We also assume that the susceptible prey population follows theta-logistic growth in the form of concave relationship suggested by R. M. Sibly, D. Barker, M. C. Denham, J. Hone and M. Pagel [“On the regulation of populations of mammals, birds, fish, and insects”, Science 309, 607 (2005)] in analyzing global population dynamics database (GPDD) for species of four taxonomic groups. Numerical simulations for the proposed model are presented for illustration of the analytical results and compared with the existing literature. Stability and bifurcation analysis of the dynamical system are well studied. Our findings suggest that in disease-free system, the predator-prey oscillations can be stabilized through the density dependent theta-logistic growth.

MSC:

92D40 Ecology
92D25 Population dynamics (general)
34C60 Qualitative investigation and simulation of ordinary differential equation models
37N25 Dynamical systems in biology
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