摘要
It has been reported that the minimal spatially extended phytoplankton-zooplankton system exhibits both temporal regular/chaotic behaviour, and spatiotemporal chaos in a patchy environment. As a further investigation by means of computer simulations and theoretical analysis, in this paper we observe that the spiral waves may exist and the spatiotemporal chaos emerge when the parameters are within the mixed Turing-Hopf bifurcation region, which arises from the far-field breakup of the spiral waves over a large range of diffusion coefficients of phytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising from the far-field breakup of spiral waves does not gradually invade the whole space of that region. Our results are confirmed by nonlinear bifurcation of wave trains, We also discuss ecological implications of these spatially structured patterns.
It has been reported that the minimal spatially extended phytoplankton-zooplankton system exhibits both temporal regular/chaotic behaviour, and spatiotemporal chaos in a patchy environment. As a further investigation by means of computer simulations and theoretical analysis, in this paper we observe that the spiral waves may exist and the spatiotemporal chaos emerge when the parameters are within the mixed Turing-Hopf bifurcation region, which arises from the far-field breakup of the spiral waves over a large range of diffusion coefficients of phytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising from the far-field breakup of spiral waves does not gradually invade the whole space of that region. Our results are confirmed by nonlinear bifurcation of wave trains, We also discuss ecological implications of these spatially structured patterns.
基金
supported by the National Natural Science Foundation of China (Grant No 60771026)
the Program for New Century Excellent Talents in University (Grant No NCET050271)
the Natural Science Foundation of Shan’xi Province, China(Grant No 2006011009)
US National Science Foundation Biocomplexity Program (DEB0421530)
LTER Program (Grant NoDEB0620482)