Plankton nutrient interaction model with effect of toxin in presence of modified traditional Holling Type II functional response

Figures & data

Table 1. The table representing thresholds and stability of steady states.

Thresholds()	()	()	()
	Asymptotically stable	Not feasible	Not feasible
	Unstable	Asymptotically stable	Not feasible
	Unstable	Unstable	Asymptotically stable

Figure 1. The equilibrium point is stable for the parametric values as given in Table 2.

Table 2. A set of parametric values.

	Constant input of nutrient	3
D	Dilution rate of nutrient	0.3
	Nutrient uptake rate for the phytoplankton	0.9
	Nutrient conversion rate for the phytoplankton	0.8
	Rate of encounter per unit of phytoplankton species	0.3
	Fraction of effort applied to foraging for plankton species	0.7
h	Handling time of the zooplankton	0.3
	Max units of phytoplankton species a zooplankton can eat per day	3
	Conversion constant (zooplankton species per unit phytoplankton species)	0.5
	Half saturation constant for phytoplankton	0.6
	Mortality rate of phytoplankton	0.15
	Mortality rate of zooplankton	0.04

Figure 2. The figure depicts oscillatory behaviour around the positive interior equilibrium of the system (2.1) for increasing from 3 to 5.5 with same set of parametric values as given in Table 2.

Figure 3. The figure depicts stable behaviour at of the system (2.1) for with same set of parametric values as given in Table 2.

Figure 4. The figure depicts oscillatory behaviour around the positive interior equilibrium of the system (2.1) for increasing D from 0.3 to 0.85 with same set of parametric values as given in Table 2.

Figure 5. The figure depicts stable behaviour at of the system (2.1) for D=0.02 with same set of parametric values as given in Table 2.

Figure 6. The figure depicts oscillatory behaviour around the positive interior equilibrium of the system (2.1) for decreasing the value of from 3 to 0.25 with same set of parametric values as given in Table 2.

Figure 7. The figure depicts stable behaviour at of the system (2.1) for G₁=0.15 with same set of parametric values as given in Table 2.

Figure 8. The figure depicts stable behaviour at of the system (2.1) for increasing the value of with same set of parametric values as given in Table 2.

Figure 9. (a) The figure depicts different steady-state behaviour of nutrient for the effect of . (b) The figure depicts different steady-state behaviour of phytoplankton for the effect of . (c) The figure depicts different steady-state behaviour of zooplankton for the effect of with other parametric values as given in Table 2.

Figure 10. (a) The figure depicts different steady-state behaviour of nutrient for the effect of D. (b) The figure depicts different steady-state behaviour of phytoplankton for the effect of D. (c) The figure depicts different steady-state behaviour of zooplankton for the effect of D with other parametric values as given in Table 2.

Figure 11. (a) The two parameter bifurcation diagram for –D with all parametric values as given in Table 2 of the system (2.1). (b) The two parameter bifurcation diagram for – with all parametric values as given in Table 2 of the system (2.1).