Sentence examples for some population models from inspiring English sources

In recent years, some researchers studied the existence of periodic solutions for some population models on time scales under the assumption of periodicity of the parameters by using Mawhin's coincidence degree theory (see [3 7]).

Open problem 1 Whether there exist some special population models when we fix same parameters and vary one special parameter there appears a series bifurcations and chaos.

However, as far as we know, there are few investigations concerned with the time-periodic solutions of equation (1.1), even though there is some literature for population models and Cahn-Hilliard [8, 9].

Open problem 2 From the above discussion, whether there exists chaos → flip bifurcation → local stability → flip bifurcation → chaos in some special population model when some parameters are fixed at the same values and one parameter is varied continuously.

In order to evaluate the previously developed population models, some model modifications needed to be made.

Indeed, by introducing stochastic environmental noise, some scholars have proposed some stochastic epidemic models [14 19], stochastic population models [20 28].

Some authors have introduced some more appropriate definitions of permanence for stochastic population models.

Recently, singular differential systems introduced by Rosenbrock [12], are studied because they have many applications in practical fields, such as non-Newtonian fluid mechanics, optimal control problems, and electrical circuits and some population growth models.

Some population genetic models have analyzed the general spatial spread of underdominant alleles (e.g., Barton 1979; Schofield 2002; Soboleva et al. 2003; Turelli 2010), but they include very simple or even no population dynamics.

The study of stochastic population models has been a focus of some scholars in recent years (see [25 41]).

Population models are traditionally formulated as population balance equations.