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Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
On linear perturbations of the Ricker model
Elena Braverman1, Damir Kinzebulatov
1Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, AB, Canada T2N 1N4. maelena@math.ucalgary.ca <maelena@math.ucalgary.ca>
Mathematical Biosciences
|June 27, 2006
Summary
This study analyzes perturbed Ricker models, finding that stable equilibria in recruitment models ensure global stability. For high growth rates, population extinction or stable two-cycle periods emerge depending on perturbation type.
Area of Science:
- Population Dynamics
- Mathematical Ecology
- Theoretical Biology
Background:
- Scramble competition models, such as the Ricker map, are fundamental in population dynamics.
- Understanding the impact of perturbations (recruitment and harvesting) on model stability is crucial.
- Previous work, including the Levin and May conjecture, provides a basis for stability analysis.
Purpose of the Study:
- To investigate the stability properties of linearly perturbed discrete-time single-species models.
- To analyze the effects of recruitment and harvesting perturbations on population dynamics.
- To explore the transition to chaos and emergent behaviors like extinction and periodic solutions.
Main Methods:
- Analysis of linearly perturbed discrete-time single-species scramble competition models.
- Examination of stability and bistability for time-independent and time-dependent parameters.
- Study of models with recruitment, harvesting, and random discrete constant perturbations.
Main Results:
- For recruitment models, local stability of the positive equilibrium implies global stability, supporting the Levin and May conjecture.
- High intrinsic growth rates lead to population extinction (depletion) or stable two-cycle periods (immigration).
- Perturbed Ricker models with time-dependent parameters exhibit extinction, persistence, and periodic solutions.
Conclusions:
- Linear perturbations significantly alter population dynamics, influencing stability and long-term outcomes.
- The Ricker model's behavior under perturbation is complex, with distinct outcomes based on growth rates and perturbation types.
- Results offer insights into ecological stability, chaos, and population persistence under environmental fluctuations.
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