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A Bifurcation Analysis of a Differential Equations Model for Mutualism
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
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Bananas and banana splits: a parametric degeneracy in the Hopf bifurcation for maps
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 byExpand
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Computing Arnol′d tongue scenarios
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 aExpand
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A route to computational chaos revisited: noninvertibility and the breakup of an invariant circle
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 attractingExpand
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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 theExpand
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Period doubling with higher-order degeneracies
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 orExpand
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The necessity of the Hopf bifurcation for periodically forced oscillators
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 forExpand
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Lighting Arnold flames: Resonance in doubly forced periodic oscillators
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 assumeExpand
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Dynamics of Nonholomorphic singular Continuations: a Case in Radial Symmetry
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 aExpand
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Nonholomorphic singular continuation: a case with radial symmetry
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 aExpand
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