Global Dynamics of a Higher Order Difference Equation with Quadratic Term

In this paper, we investigate the dynamics of following higher order difference equation x_{n+1}=A+B((x_{n})/(x_{n-m}²)) with A,B and initial conditions are positive numbers. Especially we study the boundedness, periodicity, global asymptotically stability and rate of convergence of related higher order difference equations.

Large Global Asymptotically Stability of an SEIR Epidemic Model with Distributed Time Delay

An SEIR epidemic transmission model is formulated under the assumption that the force of infection at the present time depends on the number of infectives at the past. It is shown that a desease free equilibrium is globally stable if no epidemic equilibrium point exists. Further the epidemic equilibrium (if it exists) is globally stable in the who;e state space except the neighborhood of the desease free equilibrium.