Dynamics Induced by Delay in a Nutrient-Phytoplankton Model with Multiple Delays

Figure 4

(a) Bifurcation diagram with for V.S. , where the symbol “S” denotes stable and the symbol “US” denotes unstable; (b) bifurcation diagram with for the effect of on nutrient-phytoplankton dynamics, where dashed line denotes unstable; solid line denotes stable; the green solid square is Hopf bifurcation point, dot-dashed line corresponding to in (a), blue line represents equilibrium, and red line represents amplitude of periodic solutions. (c) Bifurcation diagram with and , where the yellow solid square is Hopf bifurcation point, the blue solid circle is bifurcation point for periodic-2 solution, the magenta zone indicates the existence of periodic-2 solutions, and the cyan solid diamond denotes the value of for a phase and a time-series in the inner of (c). (d) A periodic-3 solution for phytoplankton population, where , , and .

(a)

(b)

(c)

(d)