Abstract
Stoichiometric producer–grazer models are nonsmooth due to the Liebig’s Law of Minimum and can generate new dynamics such as bistability for producer–grazer interactions. Environmental noises can be extremely important and change dynamical behaviors of a stoichiometric producer–grazer model. In this paper, we consider a stochastically forced producer–grazer model and study the phenomena of noise-induced state switching between two stochastic attractors in the bistable zone. Namely, there is a frequent random hopping of phase trajectories between attracting basins of the attractors. In addition, by applying the stochastic sensitivity function technique, we construct the confidence ellipse and confidence band to find the configurational arrangement of equilibria and a limit cycle, respectively.
Highlights
Ecological stoichiometry is the study of the balance of energy and multiple nutrients in ecological interactions (Sterner and Elser 2002)
A new method based on the stochastic sensitivity functions (SSF) technique has been proposed in Bashkirtseva et al (2010) to construct the analytical description of randomly forced equilibria and cycles of discrete-time models
We are only concerned with the first two types and explore the impact of noises existed in the environment on bistability between two interior attractors: one is for the stable equilibrium E2 or the unique stable limit cycle surrounding the unstable equilibrium E2, the other is for the stable internal equilibrium E4
Summary
P, whose balance affects organismal reproduction and growth, nutrient cycling, and trophic interactions. II functional response with all flexible parameters They found that the model has four types of bistability: between an internal equilibrium and a limit cycle, between an internal equilibrium and a boundary equilibrium, between two internal equilibria, and between a boundary equilibrium and a limit cycle. A new method based on the stochastic sensitivity functions (SSF) technique has been proposed in Bashkirtseva et al (2010) to construct the analytical description of randomly forced equilibria and cycles of discrete-time models. The aim of this paper is to study the phenomena of noise-induced transitions for model (1.1) with Holling-type II functional response by using the SSF technique. The analysis of noise-induced transitions and the construction of confidence ellipses for this model will be presented in Sect.
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