The aim of this paper is to establish conditions for the existence and uniqueness of the solution of a nonlinear integro-differential equation. Moreover, it is to propose a quadrature method in order to find an approximate solution and establish the convergence of the method. We conclude by providing the algorithm and some numerical simulation to confirm our theoretical results. [ABSTRACT FROM AUTHOR]
In this paper, the qualitative behavior of a discrete-time prey-predator model with Allee effect in prey population is discussed. Firstly, the existence of the fixed points and their topological classification are analyzed algebraically. Then, the conditions of existence for both period-doubling and Neimark-Sacker bifurcations arising from coexistence fixed point with the help of the center manifold theorem and bifurcation theory are investigated. OGY feedback control method is implemented to control chaos in the proposed model due to the emergence of bifurcations. Finally, numerical simulations are performed to support the theoretical findings. [ABSTRACT FROM AUTHOR]
We focused on traveling combustion waves that appear in a simplified, one-dimensional combustion model in porous media. The system we consider is a reaction-convection-diffusion system that can be reduced into two-dimension in order to prove traveling waves by phase plane analysis. In previous studies combustion wave velocity was assumed positive and their existence was proven. Also, all possible wave sequences that solve boundary value problems on infinite intervals with constant boundary data were identified. In this study, we generalize the previous work by including the case of negative combustion wave speed and taking the assumption that oxygen is carried faster than temperature. Moreover, we extend the classification of all possible wave sequences by performing numerical simulations using finite difference scheme. [ABSTRACT FROM AUTHOR]