Acknowledgement
The Department of Basic and Applied Sciences, NIFTEM Knowledge Centre, NIFTEM, India, Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, India and Mathematics Discipline of Khulna University, Khulna, Bangladesh has all provided invaluable assistance.
References
- A.M. Turing, The chemical basis of morphogenesis, Philos. Trans. R. Soc. Lond. B Biol. Sci. 237 (1952), 37-72. https://doi.org/10.1098/rstb.1952.0012
- J.M. Cushing, tability and Instability in Predator-Prey Models with Growth Rate Response Delays, Rocky Mountain Journal of Mathematics 9 (1979), 43-50. https://doi.org/10.1216/RMJ-1979-9-1-43
- B. Roy, S.K. Roy and M.H.A. Biswas, Effects on prey-predator with different functional responses, Int. J. Biomath. 10 (2017), 1750113-22. https://doi.org/10.1142/S1793524517501133
- S. Akter, M.S. Islam, M.H.A. Biswas and S. Mandal, tability and Instability in Predator-Prey Models with Growth Rate Response Delays, Communication in Mathematical Modeling and Applications 4 (2019), 84-94.
- M.N. Hasan, M.S. Uddin, and M.H.A. Biswas, Interactive Effects of Disease Transmission on Predator-Prey Model, Journal of Applied Nonlinear Dynamics 9 (2020), 401-413. https://doi.org/10.5890/jand.2020.09.005
- A. Aldurayhim, A. Elsonbaty, and A.A. Elsadany, Dynamics of diffusive modified Previte-Hoffman food web model, Mathematical Biosciences and Engineering 17 (2020), 4225-4256. https://doi.org/10.3934/mbe.2020234
- X. Zhang, Y. Huang, and P. Weng, Permanence and stability of a diffusive predator-prey model with disease in the prey, Computers and Mathematics with Applications 68 (2014), 1431-1445. https://doi.org/10.1016/j.camwa.2014.09.011
- X. Feng, Y. Song, J. Liu, and G. Wang, Permanence, stability, and coexistence of a diffusive predator-prey model with modified Leslie-Gower and B-D functional response, Adv. Differ. Equ. 68 (2018), 314.
- K. Manna, V. Volpert, and M. Banerjee, Dynamics of a Diffusive Two-Prey-One-Predator Model with Nonlocal Intra-Specific Competition for Both the Prey Species, Mathematics 8 (2020), 1-28. https://doi.org/10.3390/math8010001
- R. Yang,and J. Wei, Stability and bifurcation analysis of a diffusive prey-predator system in Holling type III with a prey refuge, Nonlinear Dyn. 79 (2015), 631-646. https://doi.org/10.1007/s11071-014-1691-8
- L.N. Guin, and S. Acharya, Dynamic behaviour of a reaction-diffusion predator-prey model with both refuge and harvesting, Nonlinear Dyn. 88 (2017), 1501-1533. https://doi.org/10.1007/s11071-016-3326-8
- W. Wang, Y. Cai, Y. Zhu, and Z. Guo, Allee-Effect-Induced Instability in a Reaction-Diffusion Predator-Prey Model, Abstract and Applied Analysis 487810 (2013), 1-10.
- A. Hastings, Disturbance, coexistence, history, and competition for space, Theoretical Population Biology 18 (1980), 363-373. https://doi.org/10.1016/0040-5809(80)90059-3
- A.J. Lotka, Elements of Mathematical Biology, Dover Publications, Mineola., 1956.
- A.J. Nicholson, and V.A. Bailey, The balance of animal populations, Proceedings of the Zool. Soc. of London 1 (1935), 551-598. https://doi.org/10.1111/j.1096-3642.1935.tb01680.x
- W.T. Jamieson, and J. Reis, Global behavior for the classical Nicholson-Bailey model, Journal of Mathematical Analysis and Applications 461 (2018), 492-499. https://doi.org/10.1016/j.jmaa.2017.12.071
- M. Edmunds, Defense in Animals: A Survey of Anti-predator Defenses, Longman, Harlow, 1974.
- E. Gonzalez-Olivares, and R. Ramos-Jiliberto, Dynamics consequences of prey refuges in a simple model system: more prey, fewer predators and enhanced stability, Ecological Modelling 106 (2003), 135-146. https://doi.org/10.1016/S0304-3800(03)00131-5
- L.B. Kats, and L.M. Dill, . The scent of death: Chemosensory assessment of predation risk by prey animals, Ecoscience 5 (1998), 361-394. https://doi.org/10.1080/11956860.1998.11682468
- C.S. Holling, The functional response of predators to prey density and its role in mimicry and population regulation, Mem. Entomol. Soc. Can. 45 (2003), 5-60.
- A.K. Sardar, M. Hanif, M. Asaduzzaman, and M.H.A. Biswas, Mathematical Analysis of the Two Species Lotka-Volterra Predator-Prey Inter-specific Game Theoretic Competition Model, Advanced Modeling and Optimization 18 (2016), 231-242.
- V.N. Afanasev, V.B. Kolmanowski, and V.R. Nosov, Mathematical Theory of Global Systems Design, Kluwer Academic, Dordrecht. 1996.
- K. Cheng, Uniqueness of a limit cycle for a predator-prey system, SIAM J. Math. Anal. 12 (1981), 541-548. https://doi.org/10.1137/0512047
- C.B. Huffaker, Experimental studies on predation: dispersion factors and predator-prey oscillations, Hilgardia 27 (1958), 343-383. https://doi.org/10.3733/hilg.v27n14p343
- C.B. Huffaker, K.P. Shea and S.G. Herman, Experimental studies on predation: complex dispersion and levels of food in an acarine predator-prey interaction, Hilgardia 34 (1963), 305-330. https://doi.org/10.3733/hilg.v34n09p305
- B. Dubey, and A. Patra, Optimal management of a renewable resource utilized by a population with taxation as a control variable, Nonlinear Analysis: Modelling and Control 18 (2013), 37-52. https://doi.org/10.15388/NA.18.1.14030
- J.B. Shukla, and B. Dubey, Modelling the depletion and conservation of forestry resource: Effect of population, J. Math. Biol. 36 (1997), 71-94. https://doi.org/10.1007/s002850050091
- I. Perfecto, and J. Vandermeer, Spatial pattern and ecological process in the coffee agro-forestry system, Ecology 89 (2008), 915-920. https://doi.org/10.1890/06-2121.1
- J. Crank, The Mathematics of Diffusion, Oxford:Clarendon Press, London, 1979.
- L. Zhang, and S. Fu, SNonlinear instability for a Leslie-Gower predator-prey model with cross diffusion, Abstract and Applied Analysis 2013 (2013), Article ID 854862, 13 pages.
- J.F. Zhang, W.T. Li, and Y.X. Wang, Turing patterns of a strongly coupled predator-prey system with diffusion effects, Nonlinear Analysis. Theory, Methods Applications 74 (2011), 847-858. https://doi.org/10.1016/j.na.2010.09.035
- K.N. Chueh, C.C. Conley, and J.A. Smoller, Positively invariant regions for systems of nonlinear diffusion equations, Indiana University Mathematics Journal 26 (1977), 373-392. https://doi.org/10.1512/iumj.1977.26.26029
- C.V. Pao, Quasisolutions and global attractor of reaction-diffusion systems, Nonlinear Analysis 26 (1996), 1889-1903. https://doi.org/10.1016/0362-546X(95)00058-4
- W.F. Morris, M. Mangel, and F.R. Adler, Mechanisms of pollen deposition by insect pollinators, volutionary Ecology 9 (1995), 304-317.
- L.A. Segel, and J.L. Jackson, Theoretical analysis of chemotactic movement in bacteria, Journal of Mechanochemistry and Cell Motility 2 (1973), 25-34.
- J.M. Smith, Mathematical Ideas in Biology, Cambridge University Press, Cambridge, 1968.
- Li. Shangzhi, Guo. Shangjiang, Permanence of a stochastic prey-predator model with a general functional response, Mathematics and Computers in Simulation 187 (2021), 308-336. https://doi.org/10.1016/j.matcom.2021.02.025
- Kar. Tapan Kumar, K.S. Chaudhuri, On Selective Harvesting of Two Competing Fish Species In The Presence Of Environmental Fluctuation, Natural Resource Modeling 17 (2004).
- R. Arditi, and L.R. Ginzburg, Coupling in predator-prey dynamics : ratio-dependence, J. Theort. Biol. 139 (1989), 311-326. https://doi.org/10.1016/S0022-5193(89)80211-5
- B. Dubey, and J. Hussain, Modelling the Interaction of Two Biological Species in a Polluted Environment, Journal of Mathematical Analysis and Applications 246 (2000), 58-79. https://doi.org/10.1006/jmaa.2000.6741
- M. Bandyopadhyay, and C.G. Chakrabarti, Deterministic and stochastic analysis of a non-linear prey-predator system, Journal of Biological Systems 11 (2003), 161-172. https://doi.org/10.1142/S0218339003000816
- M. Bandyopadhyay, R. Bhattacharya, and G.C. Chakrabarti, A nonlinear two species oscillatory system : bifurcation and stability analysis, Int. Jr. Math. Math. Sci. 2003 (2003), 1981-1991. https://doi.org/10.1155/S0161171203201174
- R.M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, New Jercy, 2001.
- V.N. Afanas'ev, V.B. Kolmanowski, V.R. Nosov, Mathematical Theory of Global Systems Design, Kluwer Academic, Dordrecht, 1996.