Sentence examples for solution persistence from inspiring English sources

The existence of a global positive solution, persistence, stability of the equilibria and Hopf bifurcation are studied respectively.

In the following, we mainly focus on finding the suitable condition for the existence of a random periodic solution, persistence, and extinction of (4).

Some important qualitative properties, such as the existence of a global positive solution, persistence, the local stability and global stability of the equilibria, are obtained.

end{cases}displaystyle end{aligned} (3.1) In this section, we will discuss the existence of positive solution, persistence and extinction of the species as well as the stationary distribution for stochastic system (3.1).

Many interesting results concerned with the global existence and attractivity of periodic solution, persistence and extinction of the population, etc. have been obtained; we refer to [1 4] and the references therein.

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.

The basic and important research subjects for these systems are local and global stability of the disease-free equilibrium point and the endemic equilibrium point, existence of periodic solutions, persistence and extinction of the disease, etc.

Local stability for the free periodic solution and persistence of the disease are key issues in the study of epidemic models.

In this section, we analytically prove positivity and boundedness of the solutions, the persistence, local and global stability, existence of the Hopf bifurcation by analyzing the associated characteristic transcendental equation for the model with a delay.

To incentivise our stakeholders to contribute and participate, we have to offer some solutions for persistence and some workable ideas for interoperability.

A corresponding result on persistence of strong solutions of the CH and Novikov equations and of Equation (1.1) can be found in [9, 45, 50], respectively.