Dynamics of phytoplankton-zooplankton systems with toxin producing phytoplankton

We propose periodic systems of phytoplankton-zooplankton interactions with toxin producing phytoplankton to study the effects of TPP upon extinction and persistence of the populations. Using the concept of uniform persistence, it is proved that the two populations can coexist for certain parameter regimes. The numerical investigation demonstrates that toxin producing phytoplankton may promote survival of zooplankton population on one hand and may destabilize the interactions on the other hand. Moreover, passive diffusion of both populations can simplify the dynamics of the interactions and exhibit plankton patchiness.

[1]  Peter Grindrod,et al.  Patterns and Waves: The Theory and Applications of Reaction-Diffusion Equations , 1991 .

[2]  P. Hartman.  Ordinary Differential Equations , 1965 .

[3]  V. Biktashev,et al.  Phytoplankton blooms and fish recruitment rate: Effects of spatial distribution , 2004, Bulletin of mathematical biology.

[4]  E. Phlips,et al.  The occurrence of potentially toxic dinoflagellates and diatoms in a subtropical lagoon, the Indian River Lagoon, Florida, USA , 2004 .

[5]  R. Bhattacharyya,et al.  Modelling phytoplankton allelopathy in a nutrient-plankton model with spatial heterogeneity , 2006 .

[6]  N. Britton.  Reaction-diffusion equations and their applications to biology. , 1989 .

[7]  Joydip Dhar,et al.  Role of toxin producing phytoplankton on a plankton ecosystem , 2010 .

[8]  A. Cembella,et al.  Toxigenic phytoplankton and concomitant toxicity in the mussel Choromytilus meridionalis off the west coast of South Africa , 2012 .

[9]  J. Baglama,et al.  Persistence in variable-yield nutrient-plankton models , 2003 .

[10]  A. Kremp,et al.  The toxic dinoflagellate Alexandrium ostenfeldii promotes incapacitation of the calanoid copepods Eurytemora affinis and Acartia bifilosa from the northern Baltic Sea , 2011 .

[11]  Yang Kuang,et al.  Global stability and persistence in diffusive food chains , 2001, The ANZIAM Journal.

[12]  R. Sarkar,et al.  A delay differential equation model on harmful algal blooms in the presence of toxic substances. , 2002, IMA journal of mathematics applied in medicine and biology.

[13]  Shigui Ruan,et al.  Turing instability and travelling waves in diffusive plankton models with delayed nutrient recycling , 1998 .

[14]  W. Gurney,et al.  Self-organization, scale and stability in a spatial predator-prey interaction , 2000, Bulletin of mathematical biology.

[15]  D. Roelke,et al.  Effects of inflow on harmful algal blooms: some considerations , 2011 .

[16]  Paul Waltman,et al.  Persistence in dynamical systems , 1986 .

[17]  J. Huisman,et al.  Biodiversity of plankton by species oscillations and chaos , 1999, Nature.

[18]  D. L. DeAngelis,et al.  Dynamics of Nutrient Cycling and Food Webs , 1992, Population and Community Biology Series.

[19]  John H. Steele,et al.  Some Comments on Plankton Patches , 1978 .

[20]  Edward R. Abraham,et al.  The generation of plankton patchiness by turbulent stirring , 1998, Nature.

[21]  Hugh L. MacIntyre,et al.  Environmental correlates of community composition and toxicity during a bloom of Pseudo-nitzschia spp. in the northern Gulf of Mexico , 2011 .

[22]  Linda J. S. Allen,et al.  A simple food chain with a growth inhibiting nutrient , 1999, Appl. Math. Comput..

[23]  John Brindley,et al.  Ocean plankton populations as excitable media , 1994 .

[24]  S Mandal,et al.  Toxin-producing plankton may act as a biological control for planktonic blooms--field study and mathematical modelling. , 2002, Journal of theoretical biology.

[25]  G. Hallegraeff.  A review of harmful algal blooms and their apparent global increase , 1993 .

[26]  Daniel B. Henry.  Geometric Theory of Semilinear Parabolic Equations , 1989 .

[27]  Richard P. Signell,et al.  A mechanism for offshore initiation of harmful algal blooms in the coastal Gulf of Maine , 2003 .

[28]  B Mukhopadhyay,et al.  A Delay-Diffusion Model of Marine Plankton Ecosystem Exhibiting Cyclic Nature of Blooms , 2005, Journal of biological physics.

[29]  S. Uye.  Impact of copepod grazing on the red-tide flagellate Chattonella antiqua , 1986 .

[30]  Horst R. Thieme,et al.  Mathematics in Population Biology , 2003 .

[31]  Malay Bandyopadhyay,et al.  Dynamical analysis of toxin producing Phytoplankton-Zooplankton interactions , 2009 .

[32]  Nicholas D. Alikakos,et al.  An application of the invariance principle to reaction-diffusion equations , 1979 .

[33]  Linda J. S. Allen,et al.  An introduction to mathematical biology , 2006 .