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- John S. Burke, Edgar Knobloch
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2006

The Swift-Hohenberg equation with quadratic and cubic nonlinearities exhibits a remarkable wealth of stable spatially localized states. The presence of these states is related to a phenomenon calledâ€¦ (More)

- John S. Burke, Edgar Knobloch
- Chaos
- 2007

The bistable Swift-Hohenberg equation exhibits multiple stable and unstable spatially localized states of arbitrary length in the vicinity of the Maxwell point between spatially homogeneous andâ€¦ (More)

- John S. Burke
- 2006

The Swiftâ€“Hohenberg equation with cubic and quintic nonlinearities exhibits multiple stable and unstable spatially localized states of arbitrary length in the vicinity of the Maxwell point betweenâ€¦ (More)

- Alain Bergeon, John S. Burke, Edgar Knobloch, Isabel Mercader
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2008

Homoclinic snaking is a term used to describe the back and forth oscillation of a branch of time-independent spatially localized states in a bistable, spatially reversible system as the localizedâ€¦ (More)

- Tobias M. Schneider, John F. Gibson, John S. Burke
- Physical review letters
- 2010

We demonstrate the existence of a large number of exact solutions of plane Couette flow, which share the topology of known periodic solutions but are localized in one spatial dimension. Solutions ofâ€¦ (More)

- Arik Yochelis, John S. Burke, Edgar Knobloch
- Physical review letters
- 2006

The formation of oscillons in a synchronously oscillating background is studied in the context of both damped and self-exciting oscillatory media. Using the forced complex Ginzburg-Landau equation weâ€¦ (More)

- John S. Burke
- 2007

The reversible Hopf bifurcation with 1:1 resonance holds the key to the presence of spatially localized steady states in many partial differential equations on the real line. Two different techniquesâ€¦ (More)

- John S. Burke, M. Desroches, Anna M. Barry, Tasso J. Kaper, Mark A. Kramer
- Journal of mathematical neuroscience
- 2012

Rapid action potential generation - spiking - and alternating intervals of spiking and quiescence - bursting - are two dynamic patterns commonly observed in neuronal activity. In computational modelsâ€¦ (More)

- John S. Burke, David S. Peters, Peter J. Hanson
- Environmental Biology of Fishes
- 2004

Atlantic croaker, Micropogonias undulatus, sampled from a transect along a pollution gradient show a trend of declining growth and physical condition. This trend is apparent in the mean size ofâ€¦ (More)

- M. Desroches, John S. Burke, Tasso J. Kaper, Mark A. Kramer
- Physical review. E, Statistical, nonlinear, andâ€¦
- 2012

Canards are solutions of slow-fast systems that spend long times near branches of repelling equilibria, periodic orbits, or higher-dimensional invariant sets. Here, we report on the observation of aâ€¦ (More)