Abstract
In this paper, a three species predator–prey model has been proposed incorporating nonlinear Lotka–Volterra competition between two competing species x and y. It is assumed that the growth rate of x increases due to its commensalism on z, but predator z species consumes y species as prey following Holling type II functional response. Moreover the prey refuge behavior has been considered on y species. Positivity and boundedness of solutions are shown analytically. Different equilibrium points are determined and the stability of the system has been checked around these equilibrium points. Hopf bifurcation analysis has been done with respect to the nonlinear relationship competition parameters γ12 and γ21 and other parameters p,v1,v2 and v3 respectively. Also, the Transcritical bifurcation analysis of the system with respect to γ12 and γ21 have been done. From the analysis, it can be concluded that the nonlinear relationship coefficients between two species x and y may control the instability of the proposed system. Finally, some numerical simulation results have been presented to study the actual dynamics of the proposed model.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
