In this paper, we formulate a single-species model of contraception control
with white noise on the death rate. Firstly, the uniqueness of global positive
solution of the model is proved. Secondly, uniformly bounded mean of solution
is obtained by using the Liyapunov function and Chebyshev inequality. Lastly,
stochastic global asymptotic stability of zero equilibriums is analyzed.
In this paper, the normal form analysis of quadratic-cubic Swift-Hohenberg
equation with a dissipative term is investigated by using the multiple-scale
method. In addition, we obtain Hamiltonian-Hopf bifurcations of two equilibria and homoclinic snaking bifurcations of one-peak and two-peak homoclinic
solutions by numerical simulations.
In this paper, weak and strong convergence theorems are established by
hybrid iteration method for generalized equilibrium problem and fixed point
problems of a finite family of asymptotically nonexpansive mappings in Hilbert
spaces. The results presented in this paper partly extend and improve the
corresponding results of the previous papers.
In this paper, the dynamics of a delayed phytoplankton-zooplankton model
is considered. Taking the delay due to the gestation of zooplankton as parameter, we describe the local Hopf bifurcation by center manifold theorem and
normal form, then we discuss the global existence of periodic solution. At last,
some simulations are given to support our result.
The paper deals with the strongly damped nonlinear wave equation of
Kirchhoff type. The existence of a global attractor is proven by using the decomposition, and moreover, the structure of the global attractor is established.
Our results improve the previous results.
In order to avoid the discussion of equation (1.1), this paper employs the
proof method of Liang (2012) to consider the re-weighted Nadaraya-Watson
estimation of conditional density. The established results generalize those of
De Gooijer and Zerom (2003). In addition, this paper improves the bandwidth
condition of Liang (2012).
In this paper, we aim at dynamical behaviors of a stochastic SIS epidemic
model with double epidemic hypothesis. Sufficient conditions for the extinction
and persistence in mean are derived via constructing suitable functions. We
obtain a threshold of stochastic SIS epidemic model, which determines how
the diseases spread when the white noises are small. Numerical simulations
are used to illustrate the efficiency of the main results of this article.
In this paper, a modified nonlinear dynamic inequality on time scales is
used to study the boundedness of a class of nonlinear third-order dynamic
equations on time scales. These theorems contain as special cases results for
dynamic differential equations, difference equations and $q$-difference equations.
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