A stability condition is provided for a class of vorticity boundary formulas used with the second order finite-difference numerical scheme for the vorticity-stream function formulation of the unsteady incompressible Navier-Stokes equations. These local vorticity boundary formulas are derived using the no-slip boundary condition for the velocity. A new form of these long-stencil formulas is need...

This paper presents a dynamic connection that can induce amplitude death in globally coupled oscillators. A linear analysis clarifies a local stability condition for global amplitude death. The analysis also indicates that the odd-number property, which is known in delayed feedback control, exists in global dynamic coupled oscillators. Furthermore, global amplitude death is experimentally obser...

The aim of this paper is to study the dynamics a reaction-diffusion SI (susceptible-infectious) epidemic model with nonlinear incidence rate describing transmission communicable disease between individuals. We prove that proposed has two steady states under one condition. By analyzing eigenvalues and using linearization method an appropriately constructed Lyapunov functional, we establish local...

This paper concerns network congestion control, focusing on a recently proposed “primal-dual” control law that has been shown to give local stability and desirable equilibrium properties for networks of arbitrary capacity and a fixed bound on delay. In this paper we study global stability for these non-linear, delay differential equations, focusing for simplicity on the scenario of a single flo...

A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory ...

In this work, we propose and analyze a model of Phytoplankton-Zooplankton interaction with harvesting considering that some species are exploited commercially for food. Criteria for local stability, instability and global stability are derived and some threshold harvesting levels are explored to maintain the population at an appropriate equilibrium level even if the species are exploited contin...

How does the mind coordinate local and global features of a display to allow for adaptive functioning? To answer this question, we presented adults with a speeded categorization task in which they had to decide whether two stimuli match in a local element, in their global pattern, or in neither the local nor the global feature. The trial series of reaction times were then subjected to fractal a...