The impact of alternative resources and fear on the dynamics of the food chain

[1] W. Cresswell,Predation in bird populations, J. Ornithol. 152 (2010) 251—263.[2] N.H. Fakhry and R.K. Naji, The dynamics of a square root prey-predator model with fear, Iraqi J. Sci. 61 (2020)
139–146.
[3] S. Gakkhar and R.K. Naji, On a food web consisting of a specialist and a generalist predator, J. Biol. Syst. 11
(2003a) 365–376.
[4] K. Garain, U. Kumar and P.S. Mandal,Global Dynamics in a Beddington–DeAngelis Prey–Predator Model with
Density Dependent Death Rate of Predator, Differ. Equ. Dyn. Syst. 29 (2021) 265–283.
[5] M. Haque, Ratio-Dependent Predator-Prey Models of Interacting Populations, Bull. Math. Biol. 71 (2008)430-
–452.
[6] A. Hastings and T. Powell, Chaos in the three-species food chain, Ecology 72 (1991) 896–903.
[7] C.S. Holling, The components of predation as revealed by a study of small-mammal predation of the European
pine sawfly, Can. Entomol. 91 (1959) 293–320.
[8] F. Hua, K. E. Sieving, R. J. Fletcher and C. A. Wright, Increased perception of predation risk to adults and
offspring alters avian reproductive strategy and performance, Behav. Ecol. 25 (2014) 509-–519.
[9] J. Liu, P. Lv, B. Liu and T. Zhang, Dynamics of a Predator-Prey Model with Fear Effect and Time Delay,
Complex. 2021 (2021) 16 pages.
[10] X. Liu and Y. Lou, Global dynamics of a predator–prey model, J. MATH. ANAL. APPL. 371 (2010) 323–340.
[11] J. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications, 3rd edition, Springer-Verlag,
NY, 2003.
[12] R.K. Naji and A.T. Balasim, Dynamical behavior of a three-species food chain model with Beddington–DeAngelis
functional response, Chaos Solitons Fract. 32 (2007) 1853–1866.
[13] P. Panday, N, Pal, S. Samanta and J. Chattopadhyay, Stability and bifurcation analysis of a three-species food
chain model with fear, IJBC. 28 (2018) 1850009-1-1850009-20.
[14] S.D. Peacor, B.L. Peckarsky, G.C. Trussell and J.R. Vonesh, Costs of predator-induced phenotypic plasticity: a
graphical model for predicting the contribution of nonconsumptive and consumptive effects of predators on prey,
Oecologia 171 (2012) 1–10.
[15] M.L. Rosenzweig and R.H. MacArthur, Graphical representation and stability conditions of predator-prey interactions, Am. Nat. 97 (1963) 209–223.
[16] S.K. Sasmal, Population dynamics with multiple Allee effects induced by fear factors – A mathematical study on
prey-predator interactions, Appl. Math. Model. 64 (2018) 1-–14.
[17] J.P. Suraci, M. Clinchy, L.M. Dill, D. Roberts and L.Y. Zanette, Fear of large carnivores causes a trophic cascade,
Nature Commun. 7 (2016) 1–7.
[18] R.K. Upadhyay and R.K. Naji, Dynamics of a three-species food chain model with Crowley–Martin type functional
response, Chaos Solitons Fract. 42, (2009) 1337—1346.
[19] X. Wang, L. Zanette and X. Zou, Modelling the fear effect in predator-prey interactions, J. Math. Biol. 73 (2016)
1179–1204.
[20] X. Wang, and X. Zou, Modeling the Fear Effect in Predator-Prey Interactions with Adaptive Avoidance of Predators, Bull. Math. Biol. 79 (2017) 1325—1359.
[21] L.Y. Zanette, A. F. White, M. C. Allen and M. Clinchy, Perceived predation risk reduces the 609 number of
offspring songbirds produce per year, Science, 334 (2011) 1398–1401.
[22] H. Zhang, Y. Cai, S. Fu and W. Wang, Impact of the fear effect in a prey-predator model incorporating a prey
refuge, Appl. Math. Comput. 356 (2019) 328-–337.