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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)

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)

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)

- Laurence Hao-Ran Lin, Bruce B Peckham, Harlan W Stech, John Pastor
- Journal of biological dynamics
- 2012

We consider a stoichiometric population model of two producers and one consumer. Stoichiometry can be thought of as the tracking of food quality in addition to food quantity. Our model assumes a reduced rate of conversion of biomass from producer to consumer when food quality is low. The model is open for carbon but closed for nutrient. The introduction of… (More)

In many applications of practical interest, for example, in control theory, economics, electronics and neural networks, the dynamics of the system under consideration can be modelled by an endomorphism, which is a discrete smooth map that does not have a uniquely defined inverse; one also speaks simply of a noninvertible map. In contrast to the better known… (More)

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