6533b82bfe1ef96bd128deea

RESEARCH PRODUCT

Subharmonic and homoclinic bifurcations in the driven and damped sine-Gordon system

Timoléon C. KofanéTimoléon C. KofanéLaurent NanaErnest Kaptouom

subject

BreatherMathematical analysisChaoticStatistical and Nonlinear PhysicsCondensed Matter PhysicsSignalNonlinear Sciences::Chaotic DynamicsAmplitudeClassical mechanicsBiharmonic equationHomoclinic orbitSineConstant (mathematics)Nonlinear Sciences::Pattern Formation and SolitonsMathematics

description

Abstract Chaotic responses induced by an applied biharmonic driven signal on the sine-Gordon (sG) system influenced by a constant dc-driven and the damping fields are investigated using a collective coordinate approach for the motion of the breather in the system. For this biharmonic signal, one term has a large amplitude at low frequency. Thus, the classical Melnikov method does not apply to such a system; however, we use the modified version of the Melnikov method to homoclinic bifurcations of the perturbed sG system. Additionally resonant breathers are studied using the modified subharmonic Melnikov theory. This dynamic behavior is illustrated by some numerical computations.

yearjournalcountryeditionlanguage
1999-10-01Physica D: Nonlinear Phenomena
https://doi.org/10.1016/s0167-2789(98)00312-1