Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1993-09-08
Nonlinear Sciences
Chaotic Dynamics
22 pages, plain TEX. Figures available on request
Scientific paper
We study a third-order nonlinear ordinary differential equation whose solutions, under certain specific conditions, are individual pulses. These correspond to homoclinic orbits in the phase space of the equation and we study the possible pulse types in some detail. Sufficiently close to the conditions under which a homoclinic orbit exists, the solutions take the form of trains of well-separated pulses. A measure of closeness to homoclinic conditions provides a small parameter for the development of an asymptotic solution consisting of superposed, isolated pulses. The solvability condition in the resulting singular perturbation theory is a {\its timing map} relating successive pulse spacings. This map of the real line onto itself, together with the known form of the homoclinic orbit, provides a concise and accurate solution of the equation.
BALMFORTH Neil J.
IERLEY Glenn R.
Spiegel Edward A.
No associations
LandOfFree
Chaotic Pulse Trains does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Chaotic Pulse Trains, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Chaotic Pulse Trains will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-497275