6533b850fe1ef96bd12a81a5

RESEARCH PRODUCT

Horseshoe-shaped maps in chaotic dynamics of long Josephson junction driven by biharmonic signals

Laurent NanaErnest KaptouomTimoléon C. KofanéTimoléon C. Kofané

subject

Field (physics)BreatherGeneral MathematicsApplied MathematicsChaoticGeneral Physics and AstronomyStatistical and Nonlinear PhysicsNonlinear systemClassical mechanicsBiharmonic equationConstant (mathematics)Nonlinear Sciences::Pattern Formation and SolitonsVariable (mathematics)MathematicsLong Josephson junction

description

Abstract A collective coordinate approach is applied to study chaotic responses induced by an applied biharmonic driven signal on the long Josephson junction influenced by a constant dc-driven field with breather initial conditions. We derive a nonlinear equation for the collective variable of the breather and a new version of the Melnikov method is then used to demonstrate the existence of Smale horseshoe-shaped maps in its dynamics. Additionally, numerical simulations show that the theoretical predictions are well reproduced. The subharmonic Melnikov theory is applied to study the resonant breathers. Results obtained using this approach are in good agreement with numerical simulations of the dynamics of the Poincare islands.

yearjournalcountryeditionlanguage
2000-11-01Chaos, Solitons & Fractals
https://doi.org/10.1016/s0960-0779(99)00145-9