Photosynthesis rate, salinity induced grazing rate and gestation delay as determinants of the dynamics of a realistic food chain model: a stochastic approach

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• 作者：Ujjwal Roy ; N. C. Majee ; Santanu Ray
• 关键词：Photosynthesis rate ; Salinity induced grazing rate ; Gestation delay ; Hopf ; bifurcation ; Gaussian white ; noise
• 刊名：Modeling Earth Systems and Environment
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：2
• 期：2
• 全文大小：674 KB
• 参考文献：Berryman AA (1992) The origins and evolution of predatorprey theory. Ecology 73:1530–1535CrossRef
  Ding Y, Jiang W (2011) Double Hopf bifurcation and chaos in Liu-system with delaed feedback. J Appl Anal Comput 1(3):325–349
  Ding Y, Jiang W, Yu P (2013) Double Hopf bifurcation in acontainer crane model with delayed position feedback. Appl Math Comput 219:9270–9281
  Iwasa Y, Hakoyama H, Nakamaru M, Nakanishi J (2000) Estimate of population extinction risk and its application to ecological risk management. Popul Ecol 42:73–80CrossRef
  Jana D (2014) Stabilizing effect of prey refuge and predator’s interference on the dynamics of prey with delayed growth and generalist predator with delayed gestation. Int J Ecol 2014:12. Article ID 429086. doi:10.​1155/​2014/​429086
  Jana D, Bairagi N (2013) complexity, stochasticity and the stability of predator-prey interactions. J Control Eng Technol 3(2):76–83CrossRef
  Jana D, Agrawal R, Upadhyay RK (2014) Top-predator interference and gestation delay as determinants of the dynamics of a realistic model food chain. Chaos Solitons Fractals 69:50–63CrossRef
  Jana D, Agrawal R, Upadhyay RK (2015) Dynamics of generalist predator in a stochastic environment: effect of delayed growth and prey refuge. Appl Math Comput 268:1072–1094
  Ketchum BH (1951) The exchange of fresh and salt water in tidal estuaries. J Mar Res 10:1838
  Lande R (1993) Risks of population extinction from demographic and environmental stochasticity and random catastrophes. Am Nat 142:911–927CrossRef
  Lü J, Chen G, Cheng D, Celikovsky S (2002) Bridge the gap between the Lorenz system and the Chen system. Int J Bifurc Chaos 12:2126–2917
  Ma S, Lu Q, Feng Z (2008) Double Hopf bifurcation for van der Pol–Duffing oscillator with parametric delay feedback control. J Math Anal Appl 338:993–1007CrossRef
  Mackey M, Glass L (1977) Oscillations and chaos in physiological control systems. Science 197:287–289CrossRef
  Mandal S, Ray S, Ghose PB (2012) Modelling nutrient (dissolved inorganic nitrogen) and plankton dynamics at sagarisland of Hooghly-Matla estuarine system, West Bengal, India. J Nat Resour Model 25:629–652CrossRef
  Matouk AE (2008) Dynamical analysis, feedback control synchronization of Liu dynamical system. Nonlinear Anal 69:3132–3213CrossRef
  May RM (1973) Stability in randomly fluctuating deterministic environments. Am Nat 107:621–650CrossRef
  Nisbet RM, Gurney WSC (1982) Modelling fluctuating populations. Wiley Interscience, NewYork
  Ripa J, Lundberg P, Kaitala V (1998) A general theory of environmental noise in ecological food webs. Am Nat 107:256–263CrossRef
  Ruan S (2009) On nonlinear dynamics of predator–prey models with disc rete delay. Math Model Nat Phenom 4(2):140–188CrossRef
  Samanta GP (1996) The effect of random fluctuating environment on interacting species with time delay. Int J Math Educ Sci Technol 27:13–21CrossRef
  Samanta GP, Maiti A (2003) Stochastic Gomatam model of interacting species: non-equilibrium fluuctuation and stability. Syst Anal Model Simul 43:683–692
  Schwartz IB, Billings L, Carr TW, Dykman MI (2015) Noise-induced switching and extinction in systems with delay. Phys Rev E 91:121–139CrossRef
  Song Z, Xu Z (2013) Stability switches and double Hopf bifurcation in a two-neural network system with multiple delays. Cogn Neurodyn 7:505–521CrossRef
  Turelli M (1986) Stochastic community theory: a partially guided tour. In: Hallman TG, Levin S (eds) Mathematical ecology. Springer, Berlin
  Upadhyay RK, Mukhopadhyay A, Iyengar SRK (2007) Influence of environmental noise on the dynamics of a realistic ecological model. Fluct Noise Lett 7(01):61–77CrossRef
  Valsakumar MC, Murthy KPN, Ananthakrishna G (1983) On the linearization of non-linear Langevin type stochastic differential equations. J Stat Phys 30:617–631CrossRef
  Wang Y, Wang H, Jiang W (2014) Hopf-transcritical bifurcation in toxic phytoplankton–zooplankton model with delay. J Math Anal Appl 415:574–594CrossRef
  
• 作者单位：Ujjwal Roy (1)
  N. C. Majee (1)
  Santanu Ray (2)
  
  1. Department of Mathematics, Jadavpur University, Kolkata, 700 032, India
  2. Ecological Modelling Laboratory, Department of Zoology, Visva Bharati University, Santiniketan, 731 235, India
  
• 刊物类别：Earth System Sciences; Math. Appl. in Environmental Science; Statistics for Engineering, Physics, Co
• 刊物主题：Earth System Sciences; Math. Appl. in Environmental Science; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences; Mathematical Applications in the Physical Sciences; Ec
• 出版者：Springer International Publishing
• ISSN：2363-6211

文摘

Impact of photosynthesis rate of phytoplankton, salinity induced grazing rate of zooplankton and gestation delay of zooplankton and fish population are considered in the present study. Models with delay are much more realistic, as in reality time delays occur in almost every biological situation and assume to be one of the reasons of regular fluctuations in population density. Reproduction of predator after consuming prey is not instantaneous, but mediated by some time lag required for gestation. It is observed that there is stability switches and Hopf bifurcation occurs when the delay crosses some critical value. It is observed that the quantitative level of abundance of system population depends crucially on the delay parameter if the gestation period exceeds some critical value. Also, environmental stochasticity in the form of Gaussian white-noise, plays a significant role to describe the system and its values. Numerical examples are also support the model assumption and analytical results.