Chaos in Extended Linear Arrays of Josephson Weak Links

Extended linear arrays of interacting Josephson weak links are studied by numerical simulation using the resistively shunted junction model. The minimum coupling strength for chaotic behavior is determined as a function of the number of links. This strength is found to diminish steadily with increasing number, despite the inclusion of only nearest-neighbor interaction. The implications for Josephson technology are briefly discussed. Mathematically, the results are a confirmation of the Ruelle-Takens scenario for chaos

Self-Resonance in Cylindrical Josephson Junctions

The I-V characteristics of self-resonant cylindrical Josephson junctions in the presence of parallel applied magnetic fields have been calculated using a first-order perturbation technique

Mutual Voltage Locking in Linear Arrays of Josephson Weak Links

A linear array of superconducting weak links with a common bias current can exhibit synchronization provided there is nearest-neighbor coupling between the links. A perturbation method is applied to the equations governing this system, and the results indicate how the domain of locking depends on various parameters. Numerical simulations confirm the predicted behavior

Chaotic Behavior in an Array of Coupled Josephson Weak Links

Using the resistively shunted junction model, an array of three resistively coupled, noncapacitive, Josephson weak links, driven only by dc bias currents, is studied for the existence of chaos. This system represents one of the set of three simplest Josephson systems that, in principle, can have chaotic dynamics. The results attest to the validity of the Ruelle-Takens-Newhouse scenario for the onset of chaos

Chaotic Behavior in Coupled Superconducting Weak Links

Computer simulations have been carried out for a system consisting of a pair of coupled superconducting weak links described by a noncapacitive, resistively shunted equivalent circuit. Both dc and ac bias currents are assumed for each link. It is found that for certain ranges of ac amplitude, chaotic behavior occurs. Coupling is crucial to this result—without it no chaos will appear

Subharmonic Locking in Josephson Weak Links

After some controversy, it has been shown that subharmonic voltage (phase) locking does not exist in the ac-driven overdamped resistively shunted junction model of a Josephson weak link. We predict that for a very similar system of a pair of coupled links without ac drive, mutual subharmonic locking can take place. We demonstrate our thesis both by a careful numerical simulation of the exact equations of the model and by a second-order analytical perturbation calculation based on the coupling parameter

Analog Simulation of Coupled Superconducting Weak Links: Locking and Chaos

An improved analog simulator has been developed for the study of resistively coupled pairs of superconducting weak links. Sets of I-V characteristics, obtained with the aid of this circuit under dc bias conditions, indicate the dependence of certain features, including the voltage locking zone, on system parameters. Chaos has been observed when ac bias is also present and, for the first time, a state diagram for the system has been determined

Estimating the Fractal Dimension, K_2-entropy, and the Predictability of the Atmosphere

The series of mean daily temperature of air recorded over a period of 215 years is used for analysing the dimensionality and the predictability of the atmospheric system. The total number of data points of the series is 78527. Other 37 versions of the original series are generated, including ``seasonally adjusted'' data, a smoothed series, series without annual course, etc. Modified methods of Grassberger and Procaccia are applied. A procedure for selection of the ``meaningful'' scaling region is proposed. Several scaling regions are revealed in the ln C(r) versus ln r diagram. The first one in the range of larger ln r has a gradual slope and the second one in the range of intermediate ln r has a fast slope. Other two regions are settled in the range of small ln r. The results lead us to claim that the series arises from the activity of at least two subsystems. The first subsystem is low-dimensional (d_f=1.6) and it possesses the potential predictability of several weeks. We suggest that this subsystem is connected with seasonal variability of weather. The second subsystem is high-dimensional (d_f>17) and its error-doubling time is about 4-7 days. It is found that the predictability differs in dependence on season. The predictability time for summer, winter and the entire year (T_2 approx. 4.7 days) is longer than for transition-seasons (T_2 approx. 4.0 days for spring, T_2 approx. 3.6 days for autumn). The role of random noise and the number of data points are discussed. It is shown that a 15-year-long daily temperature series is not sufficient for reliable estimations based on Grassberger and Procaccia algorithms.Comment: 27 pages (LaTex version 2.09) and 15 figures as .ps files, e-mail: [email protected]

Computer codes for computational assistance in the study of asymptotic stability

AbstractThe Routh-Hurwitz, Liénard-Chipart and Stodola criteria are reviewed and then combined into an algorithm in order to represent efficiently Liapunov's sufficient conditions for asymptotic stability. Three computer subprograms, which were written in CDC Extended FORTRAN IV to encode this algorithm, are presented. To assist the user further, one of the routines computes the coefficients of a characteristic polynomial by the method of Leverrier. As a demonstration of the computational assistance provided by this software package, the nine-dimensional domain of asymptotic stability of a system of four o.d.e.s is estimated; these equations have been put forth by other authors to simulate the moose and wolf interactions on Isle Royale, Michigan