Crisis-Induced Intermittency and Melnikov Scale Factor.
Crisis-Induced Intermittency and Melnikov Scale Factor.
(293 K)
Franaszek, M.; Simiu, E.
Physics Letters A, Vol. 205, 137-142, September 11,
1995.
Keywords:
building technology; chaos; control theory;
intermittency; melnikov function; nonlinear dynamical
systems
Abstract:
We study the post-crucial behavior of a perturbed
bistable Hamiltonian system to which the Melnikov
approach is applicable under the assumption that the
pertubation is asymptocially small. We examine the case
of perturbations that are sufficiently large to cause
chaotic transport between space regions associated with
the system's potential wells. The main results are:
(1) a small additional harmonic excitation can cause
substantial changes in the system's mean residence time,
and (2) the dependence of the magnitude of these changes
on the additional excitation's frequency is similar to
the dependence on frequency of the system's Melnikov
scale factor. We discuss the relevance of these results
to the design of efficient, Melnikov-based open loop
controls aimed at increasing the mean residence time for
the stochastically excited counterpart of the system.
