Journal of
Ecology and The Natural Environment

  • Abbreviation: J. Ecol. Nat. Environ.
  • Language: English
  • ISSN: 2006-9847
  • DOI: 10.5897/JENE
  • Start Year: 2009
  • Published Articles: 389

Review

Possibility of species extinction in the periodical forced prey-predator model

Aldona Krupska
Institute of Molecular Physics PAS, M. Smoluchowskiego 17, 60-179 PoznaÅ„, Poland.
Email: [email protected] or [email protected]

  •  Accepted: 17 April 2013
  •  Published: 31 May 2013

Abstract

The response of the Lotka-Volterra system forced by periodical modulation was numerically simulated in a wide frequency range. The main question is: how does the change of environment A parameter influence the behavior of such a system? The answer to this question is the main purpose of this paper. In the resonance region, the oscillation of the system fits to the forced frequency (or its harmonics) and shows that the numbers of prey and predators change significantly in time. Their populations after reaching the specified value become small and sometimes they are near zero and making the recovery of the population (e.g. of the predators) impossible. The Lotka-Volterra non-linear system, in contrast to the linear oscillatory systems (e.g. damping harmonic oscillator- RLC circuit), is very sensitive; the initial conditions of the effect of resonance chaos depend on the conditions of the system. Superposition principle, including relaxation behavior is not applicable in the nonlinear Lotka-Volterra system.

 

Key words: Population model, oscillatory inflow, nonlinearity, resonance, higher harmonics, species extinction.