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- Publications
- Influence

A Bifurcation Analysis of a Differential Equations Model for Mutualism

- W. Graves, Bruce B. Peckham, J. Pastor
- Medicine, Mathematics
- Bulletin of mathematical biology
- 26 August 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.,… Expand

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

- Bruce B. Peckham, C. E. Frouzakis, I. Kevrekidis
- Mathematics
- 1995

The set of Hopf bifurcations for a two-parameter family of maps is typically a curve in the parameter plane. The side of the curve on which the invariant circle exists is further divided by… Expand

Computing Arnol′d tongue scenarios

- Frank Schilder, Bruce B. Peckham
- Computer Science, Mathematics
- J. Comput. Phys.
- 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… Expand

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

- C. Frouzakis, I. Kevrekidis, Bruce B. Peckham
- Mathematics
- 25 January 2003

Abstract 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… Expand

Plant community dynamics, nutrient cycling, and alternative stable equilibria in peatlands.

- J. Pastor, Bruce B. Peckham, S. Bridgham, J. Weltzin, J. Chen
- Medicine, Biology
- The American naturalist
- 1 November 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… Expand

Period doubling with higher-order degeneracies

- Bruce B. Peckham, Ioannis G. Keverkidis
- Mathematics
- 1 September 1991

A family of local difleomorphisms of ${\bf R}^n$ can undergo a period doubling (flip) bifurcation as an eigenvalue of a fixed point passes through $ - 1$. This bifurcation is either supercritical or… Expand

The necessity of the Hopf bifurcation for periodically forced oscillators

- Bruce B. Peckham
- Mathematics
- 1 May 1990

By varying the forcing frequency and amplitude of a periodically forced planar oscillator, the author obtains a rich variety of responses. Whenever the resonance regions that are known to exist for… Expand

Lighting Arnold flames: Resonance in doubly forced periodic oscillators

- Bruce B. Peckham, I. Kevrekidis
- Mathematics
- 1 March 2002

We study doubly forced nonlinear planar oscillators: whose forcing frequencies have a fixed rational ratio: ?1 = (m/n)?2. After some changes of parameter, we arrive at the form we study: We assume… Expand

Dynamics of Nonholomorphic singular Continuations: a Case in Radial Symmetry

- Brett Bozyk, Bruce B. Peckham
- Computer Science, Mathematics
- Int. J. Bifurc. Chaos
- 12 December 2013

This paper is primarily a study of special families of rational maps of the real plane of the form: where the dynamic variable z ∈ ℂ, and ℂ is identified with ℝ2. The parameter β is complex; n is a… Expand

Nonholomorphic singular continuation: a case with radial symmetry

- Brett Bozyk, Bruce B. Peckham
- Mathematics
- 2013

z 7→ z + c+ β/z, where the dynamic variable z ∈ C, and C is identified with R. The parameters c and β are complex; n and d are positive integers. For β small, this family can be considered a… Expand

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