Bao, Jianhai and Mao, Xuerong and Yin, George and Yuan, Chenggui (2011) *Competitive Lotka-Volterra population dynamics with jumps.* Nonlinear Analysis: Theory, Methods and Applications, 74 (17). pp. 6601-6616. ISSN 0362-546X

## Abstract

This paper considers competitive Lotka-Volterra population dynamics with jumps. The contributions of this paper are as follows. (a) We show stochastic differential equation (SDE) with jumps associated with the model has a unique global positive solution; (b) We discuss the uniform boundedness of $p$th moment with $p>0$ and reveal the sample Lyapunov exponents; (c) Using a variation-of-constants formula for a class of SDEs with jumps, we provide explicit solution for 1-dimensional competitive Lotka-Volterra population dynamics with jumps, and investigate the sample Lyapunov exponent for each component and the extinction of our $n$-dimensional model.

Item type: | Article |
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ID code: | 40711 |

Keywords: | variation-of-constants formula, Lotka–Volterra model, jumps, stochastic boundedness, Lyapunov exponent, extinction, Probabilities. Mathematical statistics, Analysis, Applied Mathematics |

Subjects: | Science > Mathematics > Probabilities. Mathematical statistics |

Department: | Faculty of Science > Mathematics and Statistics |

Related URLs: | |

Depositing user: | Pure Administrator |

Date Deposited: | 02 Aug 2012 16:27 |

Last modified: | 05 Sep 2014 17:10 |

URI: | http://strathprints.strath.ac.uk/id/eprint/40711 |

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