Stability of predation models with time delay

Summary

A computational method for determining regions of local stability of a system with time delay by looking for the regions of stability in terms of regions of unconditional stability, then the transition curves between stable and unstable sectors are computed.

Keywords

Stability (learning theory), Mathematics, Predation, Applied mathematics, Control theory (sociology)

References

Stability techniques for continuous linear systemsAllan M. Krall — 1965
Stability of stage-structured population modelsFred Brauer, Zhien Ma — 1987
Age-dependent predation is not a simple process. I. Continuous time modelsAlan Hastings — 1983
Time‐Delay Versus Stability in Population Models with Two and Three Trophic LevelsRobert M. May — 1973
Time Lag in Prey‐Predator Population ModelsPeter J. Wangersky, W. J. Cunningham — 1957
Discrete delay, distributed delay and stability switchesKenneth L. Cooke, Zvi Grossman — 1982
Delays in recruitment at different trophic levels: Effects on stabilityAlan Hastings — 1984
Delayed responses and stability in two-species systemsK. Gopalsamy — 1984
Stability and Complexity in Model EcosystemsMay Rm — 2019
Elements of Physical Biology.E. W. Kopf, Alfred J. Lotka — 1925
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Differential-Difference EquationsRichard Bellman, Kenneth L. Cooke, Richard Bellman — 1963
Elements of Physical Biology.R. D. Carmichael, Alfred J. Lotka — 1926
Stability and Complexity in Model EcosystemsRobert M. May — 2001
Elements of Physical Biology1925

Cited by

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Permanence and global attractivity of delay diffusive prey-predator systems with the michaelis-menten functional responseHai‐Feng Huo — 2005
Stability of a Nonautonomous Two-Species Diffusive Model with Discrete DelaysZutao Hao, Anping Liu, Xinlei Yi — 2010
Persistence and global stability for nonautonomous predator-prey system with diffusion and time delayXinyu Song, Lansun Chen — 1998
Global analysis of an impulsive delayed Lotka–Volterra competition systemYonghui Xia — 2011
Harmless delays for uniform persistenceWang Wendi, Zhien Ma — 1991
Uniform persistence and global attractivity for nonautonomous competitive systems with nonlinear dispersion and delaysXinyu Song, Jinǵan Cui — 2003
Harmless delays and global attractivity for nonautonomous predator-prey system with dispersion☆Xinyu Song, Lansun Chen — 2000
Asymptotically periodic solution of N-species cooperation system with time delayFengying Wei, Ke Wang — 2006
Global stability of Volterra models with time delayXiaoqing Weng, Zhien Ma, H. I. Freedman — 1991
Hopf bifurcation and global stability for a delayed predator-prey system with stage structure for predatorShujing Gao, Lansun Chen, Zhidong Teng — 2008
Stability and travelling waves for a time-delayed population system with stage structureLiang Zhang, Bingtuan Li, Jin Shang — 2012
On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay ⁄Shigui Ruan — 2009
A nonautonomous predator-prey system with stage structure and double time delaysJiaoyan Wang, Qishao Lu, Zhaosheng Feng — 2009
Stability for a competitive Lotka-Volterra system with delaysZhen Jin, Zhien Ma — 2002
Persistence and Global Stability on Competition System with Time-DelayHsin‐Chih Chen, Chao-Pao Ho — 2003
Absolute stability, conditional stability and bifurcation in Kolmogrov-type predator-prey systems with discrete delaysShigui Ruan — 2001
On Nonlinear Dynamics of Predator-Prey Models with Discrete DelayShigui Ruan — 2009
Permanence and Global Attractivity of Delay Diffusive Prey-Predator Systems with the Michaelis-Menten Functional ResponseHaifeng Huo — 2005
Zhien Ma's contributions to dynamical systems, ecotoxicology and epidemiology - A scientific leader,F. Brauer, C. Castillo-Chavez, T. Hallam — 2006

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