Stability switches and chaos induced by delay in a reaction-diffusion nutrient-plankton model

References

• Medvinsky AB, Petrovskii SV, Tikhonova IA, et al. Spatiotemporal complexity of plankton and fish dynamics. SIAM Rev. 2002;44:311–370. doi: 10.1137/S0036144502404442
   Web of Science ®Google Scholar
• Mukhopadhyay B, Bhattacharyya R. Modelling phytoplankton allelopathy in a nutrient-plankton model with spatial heterogeneity. Ecol Model. 2006;198:163–173. doi: 10.1016/j.ecolmodel.2006.04.005
   Web of Science ®Google Scholar
• Hallegraeff GM. A review of harmful algal blooms and their apparent global increase. Phycologia. 1993;32:79–99. doi: 10.2216/i0031-8884-32-2-79.1
   Web of Science ®Google Scholar
• Chen QW, Mynett AE. Modelling algal blooms in the Dutch coastal waters by integrated numerical and fuzzy cellular automata approaches. Ecol Model. 2006;199:73–81. doi: 10.1016/j.ecolmodel.2006.06.014
   Web of Science ®Google Scholar
• Hecky RE, Kilham P. Nutrient limitation of phytoplankton in freshwater and marine environments: a review of recent evidence on the effects of enrichment. Limnol Oceanogr. 1988;33:796–822.
   Web of Science ®Google Scholar
• Dacey JWH, Wakeham SG. Oceanic dimethylsulfide: production during zooplankton grazing on phytoplankton. Science. 1986;233:1314–1316. doi: 10.1126/science.233.4770.1314
   PubMed Web of Science ®Google Scholar
• Vanni MJ. Effects of nutrients and zooplankton size on the structure of a phytoplankton community. Ecology. 1987;68:624–635. doi: 10.2307/1938467
   Web of Science ®Google Scholar
• Dai CJ, Yu HG, Guo Q, et al. Dynamics induced by delay in a nutrient-phytoplankton model with multiple delays. Complexity. 2019;2019:3879626.
   Google Scholar
• Edwards AE, Brindley J. Zooplankton mortality and the dynamical behaviour of plankton population models. Bull Math Biol. 1999;61:303–339. doi: 10.1006/bulm.1998.0082
   PubMed Web of Science ®Google Scholar
• Mandal A, Tiwari PK, Pal S. A nonautonomous model for the effects of refuge and additional food on the dynamics of phytoplankton-zooplankton system. Ecol Complex. 2021;46:100927. doi: 10.1016/j.ecocom.2021.100927
   Web of Science ®Google Scholar
• Guo Q, Wang Y, Dai CJ, et al. Dynamics of a stochastic nutrient-plankton model with regime switching. Ecol Model. 2023;477:110249. doi: 10.1016/j.ecolmodel.2022.110249
   Web of Science ®Google Scholar
• Caperon J. Time lag in population growth response of Isochrysis galbana to a variable nitrate environment. Ecology. 1969;50:188–192. doi: 10.2307/1934845
   Web of Science ®Google Scholar
• Fussmann GF, Ellner SP, Shertzer KW, et al. Crossing the Hopf bifurcation in a live predator-prey system. Science. 2000;290:1358–1360. doi: 10.1126/science.290.5495.1358
   PubMed Web of Science ®Google Scholar
• Huisman J, Thi NNP, Karl DM, et al. Reduced mixing generates oscillations and chaos in the oceanic deep chlorophyll maximum. Nature. 2006;439:322–325. doi: 10.1038/nature04245
   PubMed Web of Science ®Google Scholar
• Sherratt JA, Smith MJ. Periodic travelling waves in cyclic populations: field studies and reaction-diffusion models. J R Soc Interface. 2008;5:483–505. doi: 10.1098/rsif.2007.1327
   PubMed Web of Science ®Google Scholar
• Yuan Y. A coupled plankton system with instantaneous and delayed predation. J Biol Dyn. 2012;6:148–165. doi: 10.1080/17513758.2010.544409
   PubMed Web of Science ®Google Scholar
• Sharma A, Sharma AK, Agnihotri K. The dynamic of plankton-nutrient interaction with delay. Appl Math Comput. 2014;231:503–515. doi: 10.1016/j.amc.2014.01.042
   Web of Science ®Google Scholar
• Chen MX, Wu RC, Liu B, et al. Hopf-Hopf bifurcation in the delayed nutrient-microorganism model. Appl Math Model. 2020;86:460–483. doi: 10.1016/j.apm.2020.05.024
   Web of Science ®Google Scholar
• Agnihotri K, Kaur H. The dynamics of viral infection in toxin producing phytoplankton and zooplankton system with time delay. Chaos Solit Fract. 2019;118:122–133. doi: 10.1016/j.chaos.2018.11.018
   Web of Science ®Google Scholar
• Das K, Ray S. Effect of delay on nutrient cycling in phytoplankton-zooplankton interactions in estuarine system. Ecol Model. 2008;215:69–76. doi: 10.1016/j.ecolmodel.2008.02.019
   Web of Science ®Google Scholar
• Chen SS, Shi JP, Wei JJ. Time delay-induced instabilities and Hopf bifurcations in general reaction-diffusion systems. J Nonlinear Sci. 2013;23:1–38. doi: 10.1007/s00332-012-9138-1
   Web of Science ®Google Scholar
• Song YL, Wei JJ. Local Hopf bifurcation and global periodic solutions in a delayed predator-prey system. J Math Anal Appl. 2005;301:1–21. doi: 10.1016/j.jmaa.2004.06.056
   Web of Science ®Google Scholar
• Bentounsi M, Agmour I, Achtaich N, et al. The Hopf bifurcation and stability of delayed predator-prey system. Comput Appl Math. 2018;37:5702–5714. doi: 10.1007/s40314-018-0658-7
   Google Scholar
• Thakur NK, Ojha A, Tiwari PK, et al. An investigation of delay induced stability transition in nutrient-plankton systems. Chaos Solit Fract. 2021;142:110474. doi: 10.1016/j.chaos.2020.110474
   Web of Science ®Google Scholar
• Wang BB, Zhao M, Dai CJ, et al. Dynamics analysis of a nutrient-plankton model with a time delay. Discrete Dyn Nat Soc. 2016;2016:9797624.
   Web of Science ®Google Scholar
• Shu HY, Hu X, Wang L, et al. Delay induced stability switch, multitype bistability and chaos in an intraguild predation model. J Math Biol. 2015;71:1269–1298. doi: 10.1007/s00285-015-0857-4
   PubMed Web of Science ®Google Scholar
• Adak D, Bairagi N, Hakl R. Chaos in delay-induced Leslie-Gower prey-predator-parasite model and its control through prey harvesting. Nonlinear Anal Real World Appl. 2020;51:102998. doi: 10.1016/j.nonrwa.2019.102998
   Web of Science ®Google Scholar
• Holmes EE, Lewis MA, Banks JE, et al. Partial differential equations in ecology: spatial interactions and population dynamics. Ecology. 1994;75:17–29. doi: 10.2307/1939378
   Web of Science ®Google Scholar
• Segel LA, Jackson JL. Dissipative structure: an explanation and an ecological example. J Theor Biol. 1972;37:545–559. doi: 10.1016/0022-5193(72)90090-2
   PubMed Web of Science ®Google Scholar
• Zhao QY, Liu ST, Niu XL. Dynamic behavior analysis of a diffusive plankton model with defensive and offensive effects. Chaos Solit Fract. 2019;129:94–102. doi: 10.1016/j.chaos.2019.08.015
   Web of Science ®Google Scholar
• Han RJ, Dai BX. Spatiotemporal pattern formation and selection induced by nonlinear cross-diffusion in a toxic-phytoplankton-zooplankton model with allee effect. Nonlinear Anal Real World Appl. 2019;45:822–853. doi: 10.1016/j.nonrwa.2018.05.018
   Web of Science ®Google Scholar
• Upadhyay RK, Volpert V, Thakur NK. Propagation of turing patterns in a plankton model. J Biol Dyn. 2012;6:524–538. doi: 10.1080/17513758.2012.655327
   PubMed Web of Science ®Google Scholar
• Dai CJ, Zhao M, Yu HG, et al. Delay-induced instability in a nutrient-phytoplankton system with flow. Phys Rev E. 2015;91:032929. doi: 10.1103/PhysRevE.91.032929
   Web of Science ®Google Scholar
• Agmour I, Baba N, Bentounsi M, et al. Mathematical study and optimal control of bioeconomic model concerning harmful dinoflagellate phytoplankton. Comput Appl Math. 2021;40:129. doi: 10.1007/s40314-021-01509-3
   Google Scholar
• Chakraborty S, Tiwari PK, Misra AK, et al. Spatial dynamics of a nutrient–phytoplankton system with toxic effect on phytoplankton. Math Biosci. 2015;264:94–100. doi: 10.1016/j.mbs.2015.03.010
   PubMed Web of Science ®Google Scholar
• Raw SN, Sahu SR. Strong stability with impact of maturation delay and diffusion on a toxin producing phytoplankton–zooplankton model. Math Comput Simulat. 2023;210:547–570. doi: 10.1016/j.matcom.2023.03.023
   Web of Science ®Google Scholar
• Liang Y, Jia Y. Stability and Hopf bifurcation of a diffusive plankton model with time-delay and mixed nonlinear functional responses. Chaos Solit Fract. 2022;163:112533. doi: 10.1016/j.chaos.2022.112533
   Web of Science ®Google Scholar
• Dai CJ, Zhao M, Yu HG. Dynamics induced by delay in a nutrient-phytoplankton model with diffusion. Ecol Complex. 2016;26:29–36. doi: 10.1016/j.ecocom.2016.03.001
   Web of Science ®Google Scholar
• Huisman J, Weissing FJ. Biological conditions for oscillations and chaos generated by multispecies competition. Ecology. 2001;82:2682–2695. doi: 10.1890/0012-9658(2001)082[2682:BCFOAC]2.0.CO;2
   Web of Science ®Google Scholar
• Moroz IM, Cropp R, Norbury J. Chaos in plankton models: foraging strategy and seasonal forcing. Ecol Model. 2016;332:103–111. doi: 10.1016/j.ecolmodel.2016.04.011
   Web of Science ®Google Scholar
• Song ZG, Zhen B, Xu J. Species coexistence and chaotic behavior induced by multiple delays in a food chain system. Ecol Complex. 2014;19:9–17. doi: 10.1016/j.ecocom.2014.01.004
   Web of Science ®Google Scholar
• Gökçe A, Yazar S, Sekerci Y. Stability of spatial patterns in a diffusive oxygen–plankton model with time lag effect. Math Comput Simulat. 2022;194:109–123. doi: 10.1016/j.matcom.2021.11.006
   Web of Science ®Google Scholar
• Hastings A, Powell T. Chaos in three-species food chain. Ecology. 1991;72:896–903. doi: 10.2307/1940591
   Web of Science ®Google Scholar
• Holling CS. Some characteristics of simple types of predation and parasitism1. Can Entomol. 1959;91:385–398. doi: 10.4039/Ent91385-7
   Google Scholar
• Ruan SG. Persistence and coexistence in zooplankton-phytoplankton-nutrient models with instantaneous nutrient recycling. J Math Biol. 1993;31:633–654. doi: 10.1007/BF00161202
   Web of Science ®Google Scholar
• Rehim M, Zhang ZZ, Muhammadhaji A. Mathematical analysis of a nutrient-plankton system with delay. SpringerPlus. 2016;5:1–22. doi: 10.1186/s40064-016-2435-7
   PubMedGoogle Scholar
• Garcés E, Vila M, Masó M, et al. Taxon-specific analysis of growth and mortality rates of harmful dinoflagellates during bloom conditions. Mar Ecol Prog Ser. 2005;301:67–79. doi: 10.3354/meps301067
   Web of Science ®Google Scholar
• Javidi M, Ahmad B. Dynamic analysis of time fractional order phytoplankton–toxic phytoplankton–zooplankton system. Ecol Model. 2015;318:8–18. doi: 10.1016/j.ecolmodel.2015.06.016
   Web of Science ®Google Scholar
• Wu JH. Symmetric functional differential equations and neural networks with memory. Trans Am Math Soc. 1998;350:4799–4838. doi: 10.1090/tran/1998-350-12
   Web of Science ®Google Scholar
• Ruan SG, Wei JJ. On the zeros of transcendental function with applications to stability of delay differential equations with two delays. Dyn Contin Discrete Impuls Syst A: Math Anal. 2003;10:863–874.
   Web of Science ®Google Scholar
• Huppert A, Blasius B, Stone L. A model of phytoplankton blooms. Am Nat. 2002;159:156–171. doi: 10.1086/324789
   PubMed Web of Science ®Google Scholar
• Steele JH, Henderson EW. The role of predation in plankton models. J Plankton Res. 1992;14:157–172. doi: 10.1093/plankt/14.1.157
   Web of Science ®Google Scholar
• Tian CR. Delay-driven spatial patterns in a plankton allelopathic system. Chaos. 2012;22:013129. doi: 10.1063/1.3692963
   PubMed Web of Science ®Google Scholar
• Li L, Liu Z. Global stability and Hopf bifurcation of a plankton model with time delay. Nonlinear Anal Theory Methods Appl. 2010;72:1737–1745. doi: 10.1016/j.na.2009.09.014
   Web of Science ®Google Scholar
• Meng XY, Li J. Stability and Hopf bifurcation analysis of a delayed phytoplankton-zooplankton model with allee effect and linear harvesting. Math Biosci Eng. 2020;17:1973–2002. doi: 10.3934/mbe.2020105
   Web of Science ®Google Scholar
• Hassard BD, Kazarinoff ND, Wan YH. Theory and applications of Hopf bifurcation. New York: Cambridge University Press; 1981.
   Google Scholar