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Title: Relaxation oscillations in predator–prey model with distributed delay

Abstract

The predator–prey model with distributed delay is stated in present paper. On the basis of geometric singular perturbation theory, the transition of the solution trajectory is illuminated, and the existence of the relaxation oscillation is proved. It is indicated the characteristic of the relaxation oscillation is dependent on the structure of the slow manifold. Moreover, the approximate expression of the relaxation oscillation and its period are obtained analytically. One case study is given to demonstrate the validity of theoretical results.

Authors:
;  [1]
  1. Shanghai Normal University, Department of Mathematics (China)
Publication Date:
OSTI Identifier:
22769378
Resource Type:
Journal Article
Journal Name:
Computational and Applied Mathematics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; DISTURBANCES; MATHEMATICAL SOLUTIONS; OSCILLATIONS; PERTURBATION THEORY; TRAJECTORIES

Citation Formats

Wang, Na, and Han, Maoan. Relaxation oscillations in predator–prey model with distributed delay. United States: N. p., 2018. Web. doi:10.1007/S40314-016-0353-5.
Wang, Na, & Han, Maoan. Relaxation oscillations in predator–prey model with distributed delay. United States. doi:10.1007/S40314-016-0353-5.
Wang, Na, and Han, Maoan. Thu . "Relaxation oscillations in predator–prey model with distributed delay". United States. doi:10.1007/S40314-016-0353-5.
@article{osti_22769378,
title = {Relaxation oscillations in predator–prey model with distributed delay},
author = {Wang, Na and Han, Maoan},
abstractNote = {The predator–prey model with distributed delay is stated in present paper. On the basis of geometric singular perturbation theory, the transition of the solution trajectory is illuminated, and the existence of the relaxation oscillation is proved. It is indicated the characteristic of the relaxation oscillation is dependent on the structure of the slow manifold. Moreover, the approximate expression of the relaxation oscillation and its period are obtained analytically. One case study is given to demonstrate the validity of theoretical results.},
doi = {10.1007/S40314-016-0353-5},
journal = {Computational and Applied Mathematics},
issn = {0101-8205},
number = 1,
volume = 37,
place = {United States},
year = {2018},
month = {3}
}