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Land
Published in Cameron La Follette , Chris Maser, Sustainability and the Rights of Nature, 2017
Cameron La Follette , Chris Maser
As a result, the United States has a significant portion of its landmass in public ownership, which gives it major opportunities to enhance and restore degraded ecological function according to the principles of the Rights of Nature. National Parks and Wildlife Refuges are explicitly managed to protect natural values and ecosystem sustainability, along with outdoor recreation.
Effects of prey refuge with Holling type IV functional response dependent prey predator model
Published in International Journal of Modelling and Simulation, 2023
Md. Sabiar Rahman, Md Sarijul Islam, Sahabuddin Sarwardi
It is well known result to the ecologists as well as mathematicians that the prey refuge has an important role to stabilize a predator prey dynamics and incorporation of prey refuge can help the prey population from extinction. To be more confirmed, one can cite Guin et al [39]., Wei and Fu [40,41]. Most of the authors [42,43] have considered a constant proportion of prey refuge depends on the prey species only. Actually, incorporation of such type of prey refuge does not bring major change in the dynamical behaviour of the system as it just replaces the refuge parameter by a new parameter . In the present article, an ecological system with Holling type IV functional response incorporating prey refuge proportional to both the population has been studied. Incorporation of such type refuge makes the model system closer to reality. It has been observed that the refuge parameter has key role to determine the behaviour of both the model system around different points of equilibria. Tables 4 and 5 show how the biomass of both the species behave with respect to increase of the refuge parameter . It is found that with respect to gradual increment of , the biomass of prey density increases and that of predator density decreases. This enriches the rate of convergence to the interior equilibrium state, which leads to fit with any natural ecosystem. Molla et al [8] did not allow intra-specific competition among predators. The model system (7) of our present study take into account intra-specific competition among predators because of there is always a competition for searching food and suitable habitat everywhere. This refinement is more realistic than that of ignoring this important behavioral trait. On the other hand, ‘paradox of enrichment’ has been studied in the present investigation. We have seen that the asymptotic behaviours of the solutions of both the model system depend on the carrying capacity . So, it is concluded that both the system (1) and (7) attain paradox of enrichment. In this respect, a comparison between our model system to some other article [11,26,44,45] has been presented in Table 1. Molla et al [11] have considered intra-specific competition in their model, they have discussed only stability and Hopf-bifurcation for both the model system. Whereas, in the present investigation we have discussed existence of transcritical bifurcation along with stability and Hopf-bifurcation with its direction for both the model system (1) and (7). It has been exhibited that the nature of Hopf bifurcation for both the systems is of sub-critical type. This trait advances our study in the sense that the previous authors like Haque et al [7], Adler et al [27], Hening and Nguyen [28] have studied intra-specific competition but they did not investigate about the nature of Hopf-bifurcation.