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The Winfree model consists of a population of globally coupled phase oscillators with randomly distributed natural frequencies. As the coupling strength and the spread of natural frequencies are varied, the various stable states of the model can undergo bifurcations, nearly all of which have been characterized previously. The one exception is the unlocking… (More)

The well-known McKendrick equations model the dynamical behavior of age-dependent populations. These equations govern, at time t, the number of individuals of age a in a population, known as the population density, and arise from a conservation law subject to constitutive assumptions for the maternity and mortality rates. In this paper, multiple scale… (More)

- Kevin Remick, Alexander Vakakis, Lawrence Bergman, D Michael Mcfarland, D Dane Quinn, Themistoklis P Sapsis
- 2013

This report describes the impulsive dynamics of a system of two coupled oscillators with essential (nonlinearizable) stiffness nonlinearity. The system considered consists of a grounded weakly damped linear oscillator coupled to a lightweight weakly damped oscillating attachment with essential cubic stiffness nonlinearity arising purely from geometry and… (More)

This text by Professor Richard Rand of Cornell University presents a variety of topics in nonlinear dynamics and perturbation methods, with an emphasis on the role of computer algebra in the analysis of such systems of differential equations. The author relies on the MACSYMA computer algebra system in performing such calculations, however the general… (More)

- Donald Dane Quinn, Office Address
- 2013

The aim of this work is to investigate conditions for optimal targeted energy transfer (TET) in a two – degree-of-freedom (DOF) nonlinear system under condition of 1:1 transient resonance capture (TRC) (Arnold, 1988; Quinn et al., 1995). In particular, we consider the following weakly damped system, 2 3 1 2 0 3 2 () () () () 0 x x x v x C x v v v x C v x λ… (More)

Synchronization is studied in a population of phase oscillators with mean-field coupling—a special case of the more general Winfree model. Each oscillator is coupled to the mean-field with a strength dependent on its phase. The uncoupled frequencies of the oscil-lators are assumed to be randomly distributed according to a specified population density. The… (More)

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