Chaos in seasonally perturbed ratio-dependent prey-predator system

被引：55
作者：
Gakkhar, S [1 ]
Naji, RK [1 ]
机构：
[1] Indian Inst Technol Roorkee, Dept Math, Roorkee 247667, Uttar Pradesh, India
来源：
CHAOS SOLITONS & FRACTALS | 2003年 / 15卷 / 01期
关键词：
D O I：
10.1016/S0960-0779(02)00114-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate the effects of periodic forcing, in the intrinsic growth rate of the prey, on the Holling-Tanner ratio-dependent prey-predator system. Lyapunov exponents, Lyapunov dimension, and Poincare section are obtained for section of parametric space for the resulting forced system. The abundance of steady state chaotic solutions is detected when seasonality is super imposed on the system, which otherwise has a globally stable equilibrium state or globally stable limit cycle. The results support the conjecture that seasons can very easily give rise to complex population dynamics. (C) 2002 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码：107 / 118
页数：12
相关论文
共 21 条
  • [1] Alligood K. T., 1997, CHAOS INTRO DYNAMICA
  • [2] [Anonymous], 2012, Practical numerical algorithms for chaotic systems
  • [3] COUPLING IN PREDATOR PREY DYNAMICS - RATIO-DEPENDENCE
    ARDITI, R
    GINZBURG, LR
    [J]. JOURNAL OF THEORETICAL BIOLOGY, 1989, 139 (03) : 311 - 326
  • [4] SEASONALITY AND PERIOD-DOUBLING BIFURCATIONS IN AN EPIDEMIC MODEL
    ARON, JL
    SCHWARTZ, IB
    [J]. JOURNAL OF THEORETICAL BIOLOGY, 1984, 110 (04) : 665 - 679
  • [5] BAKER GL, 1996, CHAOTIC DYNAMICS INT
  • [6] FREEDMAN HI, 1993, B MATH BIOL, V55, P817, DOI 10.1016/S0092-8240(05)80190-9
  • [7] GRAGNANI A, 1995, B MATH BIOL, V57, P701
  • [8] Guckenheimer J, 1986, NONLINEAR OSCILLATIO
  • [9] GLOBAL STABILITY FOR A CLASS OF PREDATOR-PREY SYSTEMS
    HSU, SB
    HUANG, TW
    [J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 1995, 55 (03) : 763 - 783
  • [10] SCENARIOS LEADING TO CHAOS IN A FORCED LOTKA-VOLTERRA MODEL
    INOUE, M
    KAMIFUKUMOTO, H
    [J]. PROGRESS OF THEORETICAL PHYSICS, 1984, 71 (05): : 930 - 937
123