Dynamics and chaos of a current driven two-dimensional Josephson junctions array under 13Φ0 magnetic field

Rafael Rangel, A. Giménez and M. Octavio

Physica A: Statistical Mechanics and its Applications, 1998, vol. 261, issue 3, 409-416

Abstract: We derive the equations of motion for a two-dimensional capacitive Josephson junctions array in the presence of both a DC current and a magnetic field f=13 of the quantum flux Φ0 . The ground state symmetry of an N×N array is assumed to hold for all currents, then by using the resistively and capacitively shunted junction equations, a model system of four-coupled non-linear second-order differential equations is derived. The system has the form βcx″+x′+∇U=0, where U is a four-dimensional potential and βc is the Stewart–McCumber parameter. The dynamics can be viewed as the motion of a massive particle sliding under the action of the potential in a four-dimensional configuration space with a friction proportional to its speed. There are three distinct branches: one below the critical current Ic where the static zero voltage solution is stable; the second branch which originates from the static solution through a Hopf bifurcation and where a total voltage develops along the direction of the applied current and across the array (instantaneous Hall voltage), (the latter means vortices moving perpendicular to the current and constitutes a flux-flow like regime); and a third branch above the synchronization current Is, where the motion of the junctions synchronizes and the motion of the vortices ceases with zero Hall voltage. For a wide range of βc, the second branch shows chaotic dynamics of extremely rich complexity. A pervasive feature is the presence of antimonotonicity, i.e., reversals of period doubling cascades.

Date: 1998
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437198002404
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:261:y:1998:i:3:p:409-416

DOI: 10.1016/S0378-4371(98)00240-4

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().