The reaction–diffusion Holling–Tanner predator–prey model with Neumann boundary condition is considered. We perform a detailed stability and Hopf bifurcation analysis and derive conditions for determining the direction of bifurcation and the stability of the bifurcating periodic solution. For partial differential equation (PDE), we consider the Turing instability of the equilibrium solutions an...

In this paper, we study the existence and uniqueness solution and investigate the conditions that make it almost-periodic solution for BAM neural networks with retarded delays. The existence of solution established by using Schauder fixed point theorem. The uniqueness established by using Banach fixed point theorem. Moreover we study the parametric stability of such a solution. Also we illustra...

Periodic elasticity problem is attractive subject and important from the theoretical and practical viewpoints. In this paper, we propose a fundamental solution method for elasticity problems of planes with one-dimensional periodic structure. The fundamental solution method [4, 15] is a numerical solver for partial differential equation problems and is widely used in science and engineering, esp...

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When an incident Herglotz wave function scatteres from a periodic Lipschitz continuous surface with Dirichlet boundary condition, then the classical (quasi-)periodic solution theory for scattering from periodic structures does not apply since the incident field lacks periodicity. Relying on the Bloch transform, we provide a solution theory in H for this scattering problem: We first prove condit...

In this paper, we implemented the Modified Iteration Perturbation Method (MIPM) for approximating the periodic behavior of a tapered beam. This problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. The solution is quickly convergent and does not need complicated calculations. Comparing the results of the MIPM with the exact solution shows that this...

The purpose of this paper is to find of the theoretical results of fixed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also, as an application, we prove the existence and uniqueness of solution for a first-order ordinary differential equation with periodic bou...

In this paper we investigate the exact peroidic wave shock solutions of the Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parametr ε and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock type solution for the cauchy problem of the in...