Table 1 - uploaded by Banamali Maji
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Default parameter values used in the numerical analysis.
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The invasion of predatory lionfish (Pterois volitans) represents a major threat to the western Atlantic coral reef ecosystems. The proliferation of venomous, fast reproducing and aggressive P. volitans in coral reefs causes severe declines in the abundance and diversity of reef herbivores. There is also widespread cannibalism amongst P. volitans po...
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... this section, we investigate the effects of various parameters on the qualitative behaviour of our system using the numerical approach of Bhattacharyya and Pal (2013) using MATLAB. The default set of parameter values, mostly taken from Bhattacharyya and Pal (2013), is given in Table 1. Under this set of parameter values, it is observed that the system becomes locally asymptotically stable at E * (cf. Figure 1). ...
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... will now verify the feasibility of the criteria of stability in Section 5. Figure 1. Time series analysis of the system for the parameters given in Table 1, the system has a stable focus at E * . ...
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... 1: If the maximal harvesting rate of adult P. volitans is increased (viz. h = 2.5), and all other parameters are as given in Table 1, then we obtain λ < 1 and 0.0503 Figure 2. Time series analysis of the system for h = 2.5 and other parameter values as given in Table 1, the system has a stable focus at E 2 . Table 1 with initial value I 1 . ...
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... 1: If the maximal harvesting rate of adult P. volitans is increased (viz. h = 2.5), and all other parameters are as given in Table 1, then we obtain λ < 1 and 0.0503 Figure 2. Time series analysis of the system for h = 2.5 and other parameter values as given in Table 1, the system has a stable focus at E 2 . Table 1 with initial value I 1 . ...
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... = 2.5), and all other parameters are as given in Table 1, then we obtain λ < 1 and 0.0503 Figure 2. Time series analysis of the system for h = 2.5 and other parameter values as given in Table 1, the system has a stable focus at E 2 . Table 1 with initial value I 1 . The system is oscillatory around E * (in black). ...
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... system is oscillatory around E * (in black). For m 1 = 1.2 and other parameters as given in Table 1, the system is locally asymptotically stable at E 2 (in blue). For m 1 = 0.5 and other parameters as given in Table 1, the system is locally asymptotically stable at E 1 (in red). ...
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... m 1 = 1.2 and other parameters as given in Table 1, the system is locally asymptotically stable at E 2 (in blue). For m 1 = 0.5 and other parameters as given in Table 1, the system is locally asymptotically stable at E 1 (in red). Figure 5. Phase plane diagram of the system projected on Pxz-space for m 2 = 7 and other parameters as given in Table 1 with initial value I 1 = (0.1, 1, 0.01). ...
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... m 1 = 0.5 and other parameters as given in Table 1, the system is locally asymptotically stable at E 1 (in red). Figure 5. Phase plane diagram of the system projected on Pxz-space for m 2 = 7 and other parameters as given in Table 1 with initial value I 1 = (0.1, 1, 0.01). The system is oscillatory around E * (in blue). ...
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... system is oscillatory around E * (in blue). For m 2 = 7 and h = 3.2, other parameters as given in Table 1, the system is locally asymptotically stable at E 2 (in black). ...
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... also obtain Figure 6. Time series analysis of the system for m 2 = 7 and other parameter values as given in Table 1, the system is oscillatory around E * (solid). For m 2 = 7, a 3 = 0.5 and other parameter values as given in Table 1, the system is LAS at E * (dotted). ...
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... series analysis of the system for m 2 = 7 and other parameter values as given in Table 1, the system is oscillatory around E * (solid). For m 2 = 7, a 3 = 0.5 and other parameter values as given in Table 1, the system is LAS at E * (dotted). satisfying the analytical conditions of stability at E * as given in Lemma 5.6 (cf. Figure 1). ...
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The invasion of predatory lionfish (Pterois volitans) represents a major threat to the western Atlantic coral reef ecosystems. The proliferation of venomous, fast reproducing and aggressive P. volitans in coral reefs causes severe declines in the abundance and diversity of reef herbivores. There is also widespread cannibalism amongst P. volitans po...
Intraguild (IG) predation (IGP) appears to offer multiple benefits for IG-predators from the viewpoints of predation and resource competition. Similarly, herbivores may also gain benefits such as resource monopoly and utilization in the form of food through IGP. We examined IGP among the larvae of two species of herbivorous beetles in eastern Japan...
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Citations
... P-volitans infestations in the Caribbean have caused serious concern due to their harmful effects on coral reefs, and a serious threat is posed to the coral reefs for rapid growth of these fishes Arias-González et al. (2011), Maji et al. (2016). Parrotfish, which are found abundantly in Caribbean reefs, feed not only on algae but also on various algal substrate, encrusting coralline, algal turf and macroalgae. ...
The number of coral reefs around the world is slowly declining due to environmental and anthropogenic reason, and Pterois volitans also put extra stress on coral reefs by decreasing the number of herbivorous fishes (parrotfish). Moreover, uncontrolled growth of algae interrupts the growth of corals since corals and algae grow together on algal turf. Here Parrotfish also play an important role in the enhancement of corals by grazing. In this paper, parrotfish and P-volitans are taken as prey and predator, respectively, and the fear effect on the dynamics of the system is investigated. The effect of prey refuge is also shown. Constant harvesting policy for both fishes is included. Stable coexistence region for two parameter spaces: Hopf bifurcation and saddle-node bifurcation, is shown and formulated for the system. Numerical simulations are illustrated to verify the authenticity of the analytical calculations.
... So, the presence of these herbivorous fishes in the reef ecosystem in turn helps in creating favorable condition for the growth of corals [14]. In addition, harvesting of invasive Pterios volitans is also considered to be an important factor to maintain the stability of the coral reef ecosystem [15]. ...
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