### Abstract

In this paper, we deal with linear and nonlinear perturbations of first-order recurrence systems with constant coefficients having infinitely many equilibria. We give sufficient conditions for the asymptotic constancy of the solutions of the perturbed equation. As a consequence of our main theorem, we obtain sufficient conditions for systems of higher-order difference equations to have asymptotic equilibrium.

Original language | English |
---|---|

Pages (from-to) | 357-368 |

Number of pages | 12 |

Journal | Computers and Mathematics with Applications |

Volume | 36 |

Issue number | 10-12 |

Publication status | Published - Nov 1998 |

### Fingerprint

### Keywords

- Asymptotic constancy
- Asymptotic equilibrium
- Equilibrium point
- Recurrence equation
- Uniform stability

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modelling and Simulation

### Cite this

*Computers and Mathematics with Applications*,

*36*(10-12), 357-368.

**Convergence to equilibria in recurrence equations.** / Agarwal, R. P.; Pituk, M.

Research output: Contribution to journal › Article

*Computers and Mathematics with Applications*, vol. 36, no. 10-12, pp. 357-368.

}

TY - JOUR

T1 - Convergence to equilibria in recurrence equations

AU - Agarwal, R. P.

AU - Pituk, M.

PY - 1998/11

Y1 - 1998/11

N2 - In this paper, we deal with linear and nonlinear perturbations of first-order recurrence systems with constant coefficients having infinitely many equilibria. We give sufficient conditions for the asymptotic constancy of the solutions of the perturbed equation. As a consequence of our main theorem, we obtain sufficient conditions for systems of higher-order difference equations to have asymptotic equilibrium.

AB - In this paper, we deal with linear and nonlinear perturbations of first-order recurrence systems with constant coefficients having infinitely many equilibria. We give sufficient conditions for the asymptotic constancy of the solutions of the perturbed equation. As a consequence of our main theorem, we obtain sufficient conditions for systems of higher-order difference equations to have asymptotic equilibrium.

KW - Asymptotic constancy

KW - Asymptotic equilibrium

KW - Equilibrium point

KW - Recurrence equation

KW - Uniform stability

UR - http://www.scopus.com/inward/record.url?scp=0032205542&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032205542&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0032205542

VL - 36

SP - 357

EP - 368

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 10-12

ER -