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In a one-parameter study of a noninvertible family of maps of the plane arising in the context of a numerical integration scheme, Lorenz studied a sequence of transitions from an attracting fixed point to " computational chaos. " As part of the transition sequence, he proposed the following as a possible scenario for the breakup of an invariant circle: the… (More)

- Harlan Stech, Bruce Peckham, John Pastor
- Theoretical population biology
- 2012

This paper presents the derivation and partial analysis of a general producer-consumer model. The model is stoichiometric in that it includes the growth constraints imposed by species-specific biomass carbon to nutrient ratios. The model unifies the approaches of other studies in recent years, and is calibrated from an extensive review of the algae-Daphnia… (More)

- John Pastor, Bruce Peckham, Scott Bridgham, Jake Weltzin, Jiquan Chen
- The American naturalist
- 2002

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… (More)

- Frank Schilder, Bruce B. Peckham
- J. Comput. Physics
- 2007

A famous phenomenon in circle-maps and synchronisation problems leads to a two-parameter bifurcation diagram commonly referred to as the Arnol ′ d tongue scenario. One considers a perturbation of a rigid rotation of a circle, or a system of coupled oscillators. In both cases we have two natural parameters , the coupling strength and a detuning parameter… (More)

Periodically forced planar oscillators are often studied by varying the two parameters of forcing amplitude and forcing frequency. For low forcing amplitudes, the study of the essential oscillator dynamics can be reduced to the study of families of circle maps. The primary features of the resulting parameter plane bifurcation diagrams are " (Arnold)… (More)

- Wendy Gruner Graves, Bruce Peckham, John Pastor
- Bulletin of mathematical biology
- 2006

We develop from basic principles a two-species differential equations model which exhibits mutualistic population interactions. The model is similar in spirit to a commonly cited model [Dean, A.M., Am. Nat. 121(3), 409-417 (1983)], but corrects problems due to singularities in that model. In addition, we investigate our model in more depth by varying the… (More)

- Richard McGehee, Bruce B. Peckham
- Experimental Mathematics
- 1994

The study of resonances in systems such as periodically forced oscillators has traditionally focused on understanding the regions in the parameter plane where these resonances occur. Resonance regions can also be viewed as projections to the parameter plane of resonance surfaces in the four-dimensional Cartesian product of the state space with the parameter… (More)

- Bruce B. Peckham
- 1998

This study provides some connections between bifurcations of one-complex-parameter complex analytic families of maps of the complex plane C and bifurcations of more general two-real-parameter families of real analytic (or C k or C ∞) maps of the real plane R 2. We perform a numerical study of local bifurcations in the families of maps of the plane given by… (More)

- Bruce B. Peckham, James Montaldi
- I. J. Bifurcation and Chaos
- 2000

This paper is primarily a numerical study of the xed-point bifurcation loci { saddle-node, period-doubling and Hopf bifurcations { present in the family: z ! f (C;A) (z; z) z + z 2 + C + Az where z is a complex dynamic (phase) variable, z its complex conjugate, and C and A are complex parameters. We treat the parameter C as a primary parameter and A as a… (More)

2 NOTE: This technical report is an expanded version of a paper by the same authors entitled " A Bifurcation Analysis of a Differential Equations Model for Mutualism. " The shorter version was accepted on August 9, 2005 and is expected to appear in the Journal of Mathematical Biology in 2006. Much of the work in both papers appeared first as part of a… (More)