### Abstract

In this paper, we consider the following logistic equation with piecewise constant arguments: {dN(t)/dt=rN(t){1-∑_{j=0} ^{m}a_{j}N([t-j])}, t≥0, m≥1, N(0)=N_{0}>0, N(-j)=N_{-j}≥0, j=1,2,...,m, where r>0, a_{0},a_{1}, ...,a_{m}≥0, ∑_{j=0} ^{m} a_{j}>0, and [x] means the maximal integer not greater than x. The sequence {N_{n}}_{n=0} ^{∞}, where N_{n}=N(n), n=0,1,2,... satisfies the difference equation N_{n+1}=N_{n}exp{ r(1-∑_{j=0} ^{m} a_{j} N_{n-j} n=0,1,2,.... Under the condition that the first term a_{0} dominates the other m coefficient s a_{i}, 1≤i≤m, we establish new sufficient conditions of the global asymptotic stability for the positive equilibrium N*= 1/(∑_{j=0} ^{m}a_{j}).

Original language | English |
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Pages (from-to) | 560-580 |

Number of pages | 21 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 294 |

Issue number | 2 |

DOIs | |

Publication status | Published - 15 Jun 2004 |

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### Keywords

- Global attractivity
- Logistic equation
- Piecewise constant arguments

### Cite this

*Journal of Mathematical Analysis and Applications*,

*294*(2), 560-580. https://doi.org/10.1016/j.jmaa.2004.02.031