A delayed fractional order food chain model with fear effect and prey refuge

Meghadri Das and G.P. Samanta

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 178, issue C, 218-245

Abstract: A delayed fractional-order prey–predator system with fear (felt by prey) effect of predator on prey population incorporating prey refuge has been proposed. We consider a three species food chain system with Holling type I functional response for the predator population including prey refuge. The existence and uniqueness of the system is studied along with non-negativity and boundedness of the solutions of proposed system. Next, local stability of the equilibria has been studied for both delayed and non-delayed systems. We have also established that the non delayed system is globally stable under some parametric restrictions. Finally we have discussed the Hopf bifurcation due to time delay and other parameters both theoretically and numerically by the help of MATLAB and MAPLE.

Keywords: Caputo fractional differential equation; Time delay; Predator–prey food chain model; Refuge; Fear effect; Stability, Hopf bifurcation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:178:y:2020:i:c:p:218-245

DOI: 10.1016/j.matcom.2020.06.015

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