Narrow Results

In this paper, a planktonic resource–consumer system with two delays is investigated and the coefficients depend on $\tau$ one of the two delays. Firstly, the property of solution and the existence of equilibrium are given. The dynamical analysis of the system including stability and Hopf bifurcation by using the delays as parameters is carried out. Both the single delay and two delays can cause the system to produce Hopf bifurcation and the stable switching phenomena may exist. Furthermore, using the crossing curve methods, we obtain the stable changes of equilibrium in two-delay parameter plane, which generalizes the results of the system that the coefficients do not depend on delay. Furthermore, the numerical simulation results show that the theoretical analyses are correct when the delays change.

Invasive fish species can be successfully grown in sewage-fed fish-ponds, especially treated sewage ponds. Fish species commonly grown in sewage fish ponds are bighead carp (Hypophthalmichthys nobilis), silver carp (Hypophthalmichthys molitrix), Nile tilapia (Oreochromis niloticus), grass carp (Ctenopharyngodon idella), common carp (Cyprinus carpio), and catfish species, such as African catfish (Clarias gariepinus) and walking catfish (Clarias batrachus). These fish are known to be invasive or potential invasive species and can tolerate extreme environments, such as those with high temperatures and wide ranges of salinity, pH, dissolved oxygen, and ammonia. Among the fish used in sewage-fed fishponds, tilapia exhibit the best survival in sewage. However, inorganic pollutants (heavy metals), organic pollutants (such as pesticides), and pathogens (such as bacteria, viruses, and parasites) in sewage cause morphological and physiological alterations in organs. Fortunately, these sewage pollutants mainly accumulate in the viscera (especially the liver and gill) and less in the muscle (the edible part of the fish). Furthermore, these undesirable pollutants and pathogens are generally within ranges suitable for human consumption. The information in this chapter is expected to serve as a reference for the management of invasive fish species.