[1]
|
K. M. Bailey and J. T. Duffy-Anderson, Fish Predation and Mortality, Encyclopedia of Ocean Sciences, (2001), 961–968.
doi: 10.1006/rwos.2001.0024.
|
[2]
|
S. Chakraborty and J. Chattopadhyay, Nutrient-phytoplankton-zooplankton dynamics in the presence of additional food source-a mathematical study, Journal of Biological Systems, 16 (2008), 547-564.
|
[3]
|
J. Chattopadhyay, R. R.Sarkar and A. Abdllaoui, A delay differential equation model on harmful algal blooms in the presence of toxic substances, IMA. J. Math. Appl. Med. Biol., 19 (2002), 137-161.
|
[4]
|
J. M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Springer-Verlag, Heidelberg, 1977.
|
[5]
|
K. Das and S. Ray, Effect of delay on nutrient cycling in phytoplankton-zooplankton interactions in estuarine system, Ecol. Model, 215 (2008), 69-76.
|
[6]
|
J. Dhar, A. K. sharma and S. Tegar, The role of delay in digestion of plankton by fish population: A fishary model, The Journal of Nonlinear Sciences and its Applications, 1 (2008), 13-19.
doi: 10.22436/jnsa.001.01.03.
|
[7]
|
B. Dubey and A. Kumar, Dynamics of prey-predator model with stage structure in prey including maturation and gestation delays, Nonlinear Dynamics, 96 (2019), 2653-2679.
|
[8]
|
J. Ghosh, B. Sahoo and S. Poria, Prey-predator dynamics with prey refuge providing additional food to predator, Chaos, Solitons and Fractals, 96 (2017), 110-119.
doi: 10.1016/j.chaos.2017.01.010.
|
[9]
|
K. Gopalsamy, Stability and Oscillations in Delay Differential Equations of Population Dynamics, Kluwer Academic, 1992.
doi: 10.1007/978-94-015-7920-9.
|
[10]
|
J. K. Hale, Ordinary Differential Equations, Wiley, New Yark, 1969.
|
[11]
|
J. K. Hale, Theory of Functional Differential Equations, Springer, Heidelberg, 1977.
|
[12]
|
M. Haque and D. Greenhalgh, When a predator avoids infected prey: a model-based theoretical study, Math. Med. Biol., 27 (2010), 75-94.
doi: 10.1093/imammb/dqp007.
|
[13]
|
J. D. Harwood and J. J.Obrycki, The role of alternative prey in sustaining predator population, in Proceedings of Second International Symposium on Biological Control of Arthropods (ed. M.S. Hoddle), 2 (2005), 453–462.
|
[14]
|
B. D. Hassard, N. D. Kazarinoff and Y. H. Wan, Theory and Application of Hopf-Bifurcation, Cambridge University Press, Cambridge, 1981.
|
[15]
|
G. R. Huxel and K. McCann, Food web stability: the influence of trophic flows across habitats, Am. Nat., 152 (1998), 460-469.
|
[16]
|
G. R. Huxel, K. McCann and G. A. Polis, Effects of partitioning allochthonous and autochthonous resources on food web stability, Ecol. Res., 17 (2002), 419-432.
|
[17]
|
R. P. Kaur, A. Sharma and A. K. Sharma, Complex dynamics of phytoplankton-zooplankton intercation system with predation and toxin liberation delay, International Journal of Grid And Distributing Computing, 12 (2019), 23-50.
|
[18]
|
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, New York, 1993.
|
[19]
|
B. Mukhopadhyay and R. Bhattacharyya, Role of gestation delay in a planktonfish model under stochastic fluctuations, Mathematical Biosciences, 215 (2008), 26-34.
doi: 10.1016/j.mbs.2008.05.007.
|
[20]
|
B. S. R. V. Prasad, M. Banerjee and P. D. N. Srinivasu, Dynamics of additional food provided predator-prey system with mutually interfering predators, Math. Biosci., 246 (2013), 176-190.
doi: 10.1016/j.mbs.2013.08.013.
|
[21]
|
M. Rehim and M. Imran, Dynamical analysis of a delay model of phytoplankton-zooplankton interaction, Applied Mathematical Modelling, 36 (2002), 638-647.
doi: 10.1016/j.apm.2011.07.018.
|
[22]
|
S. Ruan, The effect of delays on stability and persistence in plankton models, Nonlinear Analalysis, 24 (1995), 575-585.
doi: 10.1016/0362-546X(95)93092-I.
|
[23]
|
M. W. Sabelis and P. C. J. V. Rijn, When does alternative food promote biological pest control?, In Proc. Second Int. Symp. Biol. Control of Arthropods (ed. Hoddle MS), 2 (2005), 428–437.
|
[24]
|
T. Saha and M. Bandyopadhyay, Dynamical analysis of toxin producing Phytoplankton-Zooplankton interactions, Nonlinear Analysis: Real World Applications, 10 (2009), 314-332.
doi: 10.1016/j.nonrwa.2007.09.001.
|
[25]
|
B. Sahoo, Effects of Additional Foods to Predators on Nutrient-Consumer-Predator Food Chain Model, Isrnbio Mathematics, 2012.
doi: 10.5402/2012/796783.
|
[26]
|
B. Sahoo and S. Poria, Disease control in a food chain model supplying alternative food, Appl. Math. Model, 37 (2013), 5653-5663.
doi: 10.1016/j.apm.2012.11.017.
|
[27]
|
M. Sen, P. D. N. Srinivasu and M. Banerjeea, Global dynamics of an additional food provided predator-prey system with constant harvest in predators, Applied Mathematics and Computaions, 250 (2015), 193-211.
doi: 10.1016/j.amc.2014.10.085.
|
[28]
|
A. Sharma, A. K. Sharma and K. Agnihotry, The dynamic of plankton-nutrien interaction with delay, Applied Mathematics and Computation, 231 (2014), 503-515.
doi: 10.1016/j.amc.2014.01.042.
|
[29]
|
A. Sharma, A. K. Sharma and K. Agnihotri, Analysis of a toxin producing phytoplankton-zooplankton interaction with Holling IV type scheme and time delay, Nonlinear Dynamics, 81 (2015), 13-25.
doi: 10.1007/s11071-015-1969-5.
|
[30]
|
A. K. Sharma, A. Sharma and K. Agnihotry, Complex dynamic of plankton-fish interaction with quadratic harvesting and time delay, Model Earth Syst. Environ., 2 (2016), 1-17.
|
[31]
|
A. K. Sharma, A. Sharma and K. Agnihotry, Bifurcation behaviors analysis of a plankton model with multiple delays, International Journal of Biomathematics, 9 (2016), 1650086 (25 pages).
doi: 10.1142/S1793524516500868.
|
[32]
|
P. D. N Srinivasu, B. S. R. V. Prasad and M. Venkatesulu, Biological control through provision of additional food to predators: a theoretical study, Theor. Popul. Biol., 72 (2007), 111-120.
|
[33]
|
P. D. N. Srinivasu and B. S. R. V. Prasad, Time optimal control of an additional food provided predator-prey system with applications to pest management and biological conservation, J. Math. Biol., 60 (2010), 591-613.
doi: 10.1007/s00285-009-0279-2.
|
[34]
|
P. D. N. Srinivasu and B. S. R. V. Prasad, Role of quantity of additional food to predators as a control in predator-prey systems with relevance to pestmanagement and biological conservation, Bull. Math. Biol., 73 (2011), 2249-2276.
doi: 10.1007/s11538-010-9601-9.
|
[35]
|
D. Stiefs, G. A. K. van Voorn, B. W. Kooi, U. Feudel and T. Gross, Food quality in producer-grazer models: A generalized analysis, Am. Nat., 176 (2010), 367-380.
doi: 10.1086/655429.
|
[36]
|
J. N. Van Baalen, V. Krivan, P. C. J. Van Rijn and M. W. Sabelis, Alternative food, switching predators, and the persistence of predator-prey systems, Am. Nat., 157 (2001), 512-524.
doi: 10.1086/319933.
|
[37]
|
P. C. J. Van Rijn, Y. M. Van Houten and M. W. Sabelis, How plants benefit from providing food to predators even when it is also edible to herbivores, Ecology, 83 (2002), 2664-2679.
|