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...

The flow driven by a rotating end wall in a cylindrical container with aspect ratio H/R52.5 is time dependent for Reynolds numbers Re5VR/n.2700. For Reynolds numbers up to 4000 three solution branches have been identified, and we examine a solution on each one. At Re53000, the flow is axisymmetric and time periodic. At Re53500, the flow is quasiperiodic with a low-frequency modulation and suppo...

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...