Mathematical Model of an Interaction between Bears and Salmon; A Case in British Columbia

Hilda Fahlena, Jane T. M. Sahetapy-Engel, Azhary Ramadhanty, Dancent Sutanto, Eduardus Axel Wijaya, Ambar Winarni

Abstract


An interaction model for the Pacific salmon and bear population in British Columbia is discussed here. The phenomenon is shown during the salmons period of migration back to their birthplace river at the end of their life. During this returning home, a large number of bears from the nearby state come and prey on them. This predation of salmon before spawning is suspected as the cause of the decline in Salmon production. Here a dynamical model involving a specific predator-prey type interaction between Salmon and Bears is constructed in the form of a non-autonomous dynamical system, in which the transition rate from the adult state of salmon to the spawning state is positive only in the month of migration. Dynamical analysis for the stability of the coexistence equilibrium for the autonomous case is shown and sensitivity analysis for the non-autonomous the case is done numerically.

Keywords


Predator-prey, Equilibrium point, Stability analysis

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References


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DOI: http://dx.doi.org/10.5614%2Fcbms.2019.2.1.4

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This journal published by: Indonesian Bio-Mathematical Society, Pusat Pemodelan Matematika dan Simulasi, Jalan Ganesa No. 10 Bandung 40116