### Abstract

This paper is devoted to obtain the form of the solution and the qualitative properties of the following systems of a rational difference equations of order two (Formula Presented), with positive initial conditions x_{−1}, x_{0}, y_{−1} and y_{0} are nonzero real numbers. If we let u_{n} = x_{n}x_{n−1} and vn = y_{n}y_{n−1}, then these systems can be viewed as special cases of the system of the form un+1 = f (v_{n}), v_{n+1} = g(un). This system has applications in modeling population growth with age structure or the dynamics of plant-herbivore interaction. Let w_{n} = u_{2n}, we have w_{n+1} = f (g(w_{n})) ≡ h(w_{n}). At a nonzero steady state w^{∗} of the last difference equation, we have |h′^{∗})| = |f′ (g(w^{∗}))g′ (w^{∗})| = 1, indicating that the system is degenerate at this steady state.

Original language | English (US) |
---|---|

Pages (from-to) | 321-333 |

Number of pages | 13 |

Journal | Journal of Computational Analysis and Applications |

Volume | 18 |

Issue number | 2 |

State | Published - Feb 1 2015 |

### Keywords

- Difference equations
- Periodic solution
- Recursive sequences
- Stability
- System of difference equations

### ASJC Scopus subject areas

- Computational Mathematics

## Fingerprint Dive into the research topics of 'Solutions and properties of some degenerate systems of difference equations'. Together they form a unique fingerprint.

## Cite this

*Journal of Computational Analysis and Applications*,

*18*(2), 321-333.