Vol. 8, No. 4 (2019): Regular Issue

The aim of this paper is to develop the question of the regional stabilization for infinite-semilinear parabolic systems on a spatial domain Ω. precisely the study of such system on a subregion ω of Ω. We consider a decomposition of the state space via the spectral properties of the system. Then we apply this approach to regional strong and weak stabilization problem using bounded feedback. Some applications and simulations are presented.

Monotone dynamical systems theory is an efficient and powerful tool for the study of dynamical systems asymptotic behaviour. However it is rarely used in mathematical epidemiology. In this paper we present a comparison between two different approaches of convergence and stability for dynamical systems. We prove that the convergence in the sense of the monotone dynamical systems theory is equivalent to the uniform convergence in the classical Lyapunov theory. Then we provide a stability analysis of an SIS epidemiological model based on the monotone approach. Numerical simulations illustrate our theoretical results.

In this work, we propose and analyze a delayed epidemic model with logistic growth, in which the growth of susceptible individuals is governed by the logistic equation and the delay represents the latent period of the disease. Firstly, we prove that our model is mathematically and biologically well posed. In addition, the stability of equilibria and the existence of Hopf bifurcation are established. Moreover, several epidemic models existing in the previous studies are extended and generalized. Finally, some numerical simulations are given to illustrate our main results.

This paper discusses asymptotic stability and Hopf bifurcations occurs at the origin in certain two-dimensional neutral delay differential equations. We give necessary and sufficient conditions on the parameters to obtain the asymptotic stability and bifurcations. Global existence of periodic solutions is established using a global Hopf bifurcation result of Krawcewicz et al. Finally, some numerical simulations are carried out to support the analytic results. Our results are a generalization of M. Liu and X. Xu [1].

This paper is devoted to the study of the oscillatory behavior of damped second order nonlinear impulsive differential equations with variable delay. The results obtained here extend and complement to some known results in the literature.

Sufficient conditions of boundary controllability of fractional nonlocal semi-linear neutral evolution equations with impulsive conditions are demonstrated. To get the result, we employ fixed point theorem and strongly continuous semi-group theory. An application is discussed to explain the theory.

By employing the coupled nonlocal slit-strips integral boundary conditions involving Caputo derivative, we investigate the existence and uniqueness of a boundary value problem of fractional differential equations. The main result is illustrated with examples.

The Parameter OptimizationMethod was presented with analytical and numerical examples. It was shown that it is a useful tool for solving differential equations with contour conditions. The numerical procedure is based only on Runge-Kutta integration routine and on optimization techniques, both frequently used and with many developed routines, thus it was shown that this approach is accessible and practical. The method was used to solve a one-dimensional Nonlinear Schr¨odinger Equation and a nonlinear Euler- Bernoulli beam.

We report results of a numerical investigation on parameter planes of a set of four autonomous first-order nonlinear ordinary differential equations. More specifically, here are reported ten numerically computed parameter plane diagrams for a five-parameter four-dimensional system, where the dynamical behavior of each point is characterized by using the related Lyapunov exponents spectrum. Each of these parameter plane diagrams indicates parameter values for which hyperchaos, chaos, quasiperiodicity, and periodicity may be found, i.e., each of these diagrams shows delimited regions for each of these dynamical behaviors.