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  • Equilibria  (1)
  • Nonlinear stability  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Models for the effect of toxicant in single-species and predator-prey systems (1991)
    Springer
    Journal of mathematical biology 30 (1991), S. 15-30 
    Details
    ISSN: 1432-1416
    Keywords: Single-species ; Predator-prey ; Toxicants ; Equilibria ; Stability ; Periodic perturbation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Models of single-species and predator-prey systems in a polluted closed environment are developed and partially analyzed. Three cases are considered: a single influx of toxicant, a constant influx of toxicant, and a periodic pollution of the environment. In the case of single-species growth we are able to determine some local and global dynamics. In the case of predator-prey systems, we investigate the existence of steady states for a small constant influx of toxicant. On leave from Department of Mathematics, Indian Institute of Technology, Kanpur, India
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00168004
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  • 2
    Electronic Resource
    Electronic Resource
    Multispecies food webs with diffusion (1982)
    Springer
    Journal of mathematical biology 13 (1982), S. 339-344 
    Details
    ISSN: 1432-1416
    Keywords: Food web ; Functional response ; Nonlinear stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Using Liapunov's direct method, in this paper, it has been shown that the general Lotka-Volterra food web is stable without and with diffusion under each case of homogeneous reservoir and flux boundary conditions. However, for a three species food web with Holling's functional response the above general result regarding stability is not necessarily true. In such a case, conditions and regions for non-linear stability, without and with diffusion, have been derived. It is shown that such an otherwise unstable system may become stable with diffusion at least in a subregion of the positive octant of the state space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276068
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    Paper (German National Licenses)
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