A diffusive toxin producing phytoplankton model with maturation delay and three-dimensional patch

The dynamics of a diffusive toxin producing phytoplankton model with maturation delay and three-dimensional patch subject to Neumann boundary condition is investigated in this paper. The global stability of boundary equilibrium is obtained. The local stability of the coexistent equilibrium and the existence of Hopf bifurcation are investigated. The conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution are derived.

[1]  Ezio Venturino,et al.  Patchy agglomeration as a transition from monospecies to recurrent plankton blooms. , 2008, Journal of theoretical biology.

[2]  C. V. Pao,et al.  Convergence of solutions of reaction-diffusion systems with time delays , 2002 .

[3]  Yong Wang,et al.  Stability and global Hopf bifurcation in toxic phytoplankton–zooplankton model with delay and selective harvesting , 2013, Nonlinear Dynamics.

[4]  Zhong Zhao,et al.  Nonlinear modelling of the interaction between phytoplankton and zooplankton with the impulsive feedback control , 2016 .

[5]  Yongli Song,et al.  Stability, Hopf bifurcations and spatial patterns in a delayed diffusive predator-prey model with herd behavior , 2015, Appl. Math. Comput..

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

[7]  Jianjun Paul Tian,et al.  Minimal Model of Plankton Systems Revisited with Spatial Diffusion and Maturation Delay , 2016, Bulletin of mathematical biology.

[8]  J. Duinker,et al.  Das CO2-Problem und die Rolle des Ozeans , 2005, Naturwissenschaften.

[9]  Junjie Wei,et al.  Dynamics in a diffusive plankton system with delay and toxic substances effect , 2015 .

[10]  Kulbhushan Agnihotri,et al.  Analysis of a toxin producing phytoplankton–zooplankton interaction with Holling IV type scheme and time delay , 2015 .

[11]  B. Hassard,et al.  Theory and applications of Hopf bifurcation , 1981 .

[12]  Jianhong Wu.  Theory and Applications of Partial Functional Differential Equations , 1996 .

[13]  Dag O. Hessen,et al.  Morphological changes in Scenedesmus induced by substances released from Daphnia , 1993 .

[14]  Yasunori Watanabe,et al.  Heptapeptide toxins contained in natural samples of Microcystis species , 1989 .

[15]  Donald M. Anderson,et al.  Turning back the harmful red tide , 1997, Nature.