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1. Neimark–Sacker bifurcation of a third-order rational difference equation‡.

Author

He, Zhimin and Qiu, Jia

Subjects
*BIFURCATION diagrams, *BIFURCATION theory, *MATHEMATICAL models, *DIFFERENCE equations, *VALUE (Economics), *COMPUTER algorithms, *NORMAL forms (Mathematics), *COMPUTER simulation
Abstract

In this paper, we investigate the existence and direction of the Neimark–Sacker bifurcation of a third-order rational difference equation with positive parameters. Firstly, it is found that there exists a Neimark–Sacker bifurcation when the parameter passes a critical value by analysing the characteristic equation. Secondly, the explicit algorithm for determining the direction and stability of the Neimark–Sacker bifurcations is derived by using the normal form theory. Finally, computer simulations are performed to illustrate the analytical results found. [ABSTRACT FROM AUTHOR]

Published
2013
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2. A non-standard finite difference scheme for an epidemic model with vaccination.

Author

Ding, Deqiong, Ma, Qiang, and Ding, Xiaohua

Subjects
*FINITE differences, *NUMERICAL analysis, *COMPUTER simulation, *VACCINATION, *LYAPUNOV functions, *MATHEMATICAL models
Abstract

The aim of this paper is to construct a non-standard finite difference (NSFD) scheme that can be used to calculate numerical solutions for an epidemic model with vaccination. Here, the NSFD method is employed to derive a set of difference equations for the epidemic model with vaccination. We show that when, the discretized model preserves positivity and global dynamics of the continuous model. Numerical simulation illustrates the effectiveness of our results. [ABSTRACT FROM PUBLISHER]

Published
2013
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