### Abstract

This study was conducted to investigate dynamics of Lotka-Volterra equation by introducing the second derivative for change acceleration in the number of predators and prey. Lotka-Volterra equation gives a simple model to the analysis of predator-prey relationships. The results obtained were as follows. Introducing the second derivative into Lotka-Volterra equation gave the square of change rate of the number of predators and that of prey. Since the square of change rate gave positive value, the following two inequalities were given. (1) Change acceleration of the number of prey per prey was higher than the product of -β and change rate of the number of predators. (2) Change acceleration of the number of predators per predator was higher than the product of 5 and change rate of the number of prey. These two might be related to the change in the number of predators and prey. It was suggested from the present study that investigating dynamics of Lotka-Volterra equation gave inequalities showing some change aspects of predator-prey relationships.

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

Pages (from-to) | 365-367 |

Number of pages | 3 |

Journal | Journal of the Faculty of Agriculture, Kyushu University |

Volume | 54 |

Issue number | 2 |

Publication status | Published - Oct 1 2009 |

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### All Science Journal Classification (ASJC) codes

- Biotechnology
- Agronomy and Crop Science

### Cite this

*Journal of the Faculty of Agriculture, Kyushu University*,

*54*(2), 365-367.

**A preliminary investigation into dynamics of Lotka-Volterra equation.** / Shimojo, Masataka; Shao, Tao; Ishiwaka, Reiko; Tanoue, Jun; Kakihara, Hidetoshi; Sata, Chiemi; Fukudome, Hayato; Asano, Yoki; Nakano, Yutaka; Tobisa, Manabu; Masuda, Yasuhisa.

Research output: Contribution to journal › Article

*Journal of the Faculty of Agriculture, Kyushu University*, vol. 54, no. 2, pp. 365-367.

}

TY - JOUR

T1 - A preliminary investigation into dynamics of Lotka-Volterra equation

AU - Shimojo, Masataka

AU - Shao, Tao

AU - Ishiwaka, Reiko

AU - Tanoue, Jun

AU - Kakihara, Hidetoshi

AU - Sata, Chiemi

AU - Fukudome, Hayato

AU - Asano, Yoki

AU - Nakano, Yutaka

AU - Tobisa, Manabu

AU - Masuda, Yasuhisa

PY - 2009/10/1

Y1 - 2009/10/1

N2 - This study was conducted to investigate dynamics of Lotka-Volterra equation by introducing the second derivative for change acceleration in the number of predators and prey. Lotka-Volterra equation gives a simple model to the analysis of predator-prey relationships. The results obtained were as follows. Introducing the second derivative into Lotka-Volterra equation gave the square of change rate of the number of predators and that of prey. Since the square of change rate gave positive value, the following two inequalities were given. (1) Change acceleration of the number of prey per prey was higher than the product of -β and change rate of the number of predators. (2) Change acceleration of the number of predators per predator was higher than the product of 5 and change rate of the number of prey. These two might be related to the change in the number of predators and prey. It was suggested from the present study that investigating dynamics of Lotka-Volterra equation gave inequalities showing some change aspects of predator-prey relationships.

AB - This study was conducted to investigate dynamics of Lotka-Volterra equation by introducing the second derivative for change acceleration in the number of predators and prey. Lotka-Volterra equation gives a simple model to the analysis of predator-prey relationships. The results obtained were as follows. Introducing the second derivative into Lotka-Volterra equation gave the square of change rate of the number of predators and that of prey. Since the square of change rate gave positive value, the following two inequalities were given. (1) Change acceleration of the number of prey per prey was higher than the product of -β and change rate of the number of predators. (2) Change acceleration of the number of predators per predator was higher than the product of 5 and change rate of the number of prey. These two might be related to the change in the number of predators and prey. It was suggested from the present study that investigating dynamics of Lotka-Volterra equation gave inequalities showing some change aspects of predator-prey relationships.

UR - http://www.scopus.com/inward/record.url?scp=70450194249&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70450194249&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:70450194249

VL - 54

SP - 365

EP - 367

JO - Journal of the Faculty of Agriculture, Kyushu University

JF - Journal of the Faculty of Agriculture, Kyushu University

SN - 0023-6152

IS - 2

ER -