Bruce B. Peckham

Plant Community Dynamics, Nutrient Cycling, and Alternative Stable Equilibria in Peatlands

Although observational data and experiments suggest that carbon flux and storage in peatlands are controlled by hydrology and/or nutrient availability, we lack a rigorous theory to account for the roles that different plant species or life‐forms, particularly mosses, play in carbon and nutrient flux and storage and how they interact with different hydrologic sources of nutrients. We construct and analyze a model of peatlands that sheds some light on this problem. The model is a set of six coupled differential equations that define the flow of nutrients from moss and vascular plants to their litters, then to peat, and finally to an inorganic nutrient resource pool. We first analyze a simple version of this model (model 1) in which all nutrient input is from precipitation and enters the moss compartment directly, mimicking the dynamics of ombrotrophic bogs. There is a transcritical bifurcation that results in a switch of stability between two equilibrium bog communities: a moss monoculture and a community where mosses and vascular plants coexist. The bifurcation depends on the magnitudes of the input/output budget of the peatland and the life‐history traits of the plants. We generalize model 1 to model 2 by dividing nutrient inputs between precipitation and groundwater, thus also allowing the development of minerotrophic fens that receive nutrient subsidies from both groundwater and precipitation and adding intraspecific competition (self‐limitation) terms for both moss and vascular plants. Partitioning precipitation inputs between moss and the nutrient pool resulted in the greatest changes in model behavior, including the appearance of a lake and a vascular plant monoculture as well as the moss monoculture and coexistence equilibrium. As with model 1, these solutions are separated by transcritical bifurcations depending on critical combinations of parameters determining the input‐output budget of the peatland as well as the life‐history characteristics of the plant species. Model 2 also allowed for an early transient spike in vascular plant dominance followed by approach to near moss monoculture and then eventual approach to coexistence equilibrium. This generalized model mimics the broad features of successional development of peatlands from fens to bogs often found in the paleorecords of peat cores.

Period doubling with higher-order degeneracies

A family of local difleomorphisms of

Bananas and banana splits: a parametric degeneracy in the Hopf bifurcation for maps

{\bf R}^n

A route to computational chaos revisited: Noninvertibility and the breakup of an invariant circle

can undergo a period doubling (flip) bifurcation as an eigenvalue of a fixed point passes through

Real continuation from the complex quadratic family: Fixed-point bifurcation sets

- 1

ARNOLD FLAMES AND RESONANCE SURFACE FOLDS

. This bifurcation is either supercritical or subcritical, depending on the sign of a coefficient determined by higher-order terms. If this coefficient is zero, the resulting bifurcation is “degenerate.” The period doubling bifurcation with a single higher-order degeneracy is treated, as well as the more general degenerate period doubling bifurcation where a fixed point has

Resonance surfaces for forced oscillators

- 1

Dynamics of nonholomorphic singular continuations: A case in radial symmetry

eigenvalue and any number of higher-order degeneracies. The main procedure is a Lyapunov–Schmidt reduction: period-2 orbits are shown to be in one-to-one correspondence with roots of the reduced “bifurcation function,“ which has

Enrichment in a stoichiometric model of two producers and one consumer

{\bf Z}^2

Quasi-equilibrium reduction in a general class of stoichiometric producer-consumer models.

symmetry. Illustrative examples of the occurrence of the singly degenerate period doubling in the context of periodically forced planar oscillators are also presented.