Recently, Jin and Guo [34] considered the system (1.5) and analyzed some aspects of blow-up mechanism, traveling waves solution and the persistence properties.
By using the comparison principle, integral and differential inequalities, and some of analytical skills, the threshold values for the stability of the disease-free periodic solution and uniform persistence of disease are obtained.
Similar to the arguments as in the proof of [3] (Theorem 3.1), we obtain the following threshold type results on the global attractivity of the zero solution and uniform persistence for (1.2).
It was selected in this study as a model anionic dye due to its high solubility in aqueous solution and its persistence once it is discharged into natural environment.
The main contributions of this article are as follows: (a) the existence of the global positive solution and the persistence of system (1.2) are discussed in detail; (b) the Hopf bifurcation analysis of system (1.2) is provided; (c) the Lyapunov function is constructed to complete the proof of global stability of the equilibria.
Moreover, the dynamic behaviors on the existence of positive solutions, periodic solutions, persistence, permanence, oscillation and stability of Nicholson's blowflies model (1.2) and its analogous equations have been studied extensively.
(3) in which they obtained some important qualitative properties, including the existence of the global positive solution, the dissipation and persistence of the two species, the local and global asymptotic stability of the constant equilibria, and Hopf bifurcation around the interior constant equilibrium.
Positivity of solutions and uniform persistence of system are studied.
The authors showed the asymptotic smoothness of solutions and uniform persistence of system (1.1).
But novel and big problems should compel novel solutions and not persistence of historical artifact.
