Magnetic Field Effect in a Two-dimensional Array of Short Josephson Junctions

We study analytically the effect of a constant magnetic field on the dynamics of a two dimensional Josephson array. The magnetic field induces spatially dependent states and coupling between rows, even in the absence of an external load. Numerical simulations support these conclusions

Disorder and Synchronization in a Josephson Junction Plaquette

We describe the effects of disorder on the coherence properties of a 2 x 2 array of Josephson junctions (a plaquette ). The disorder is introduced through variations in the junction characteristics. We show that the array will remain one-to-one frequency locked despite large amounts of the disorder, and determine analytically the maximum disorder that can be tolerated before a transition to a desynchronized state occurs. Connections with larger N x M arrays are also drawn

Emergent global oscillations in heterogeneous excitable media: The example of pancreatic beta cells

Using the standard van der Pol-FitzHugh-Nagumo excitable medium model I demonstrate a novel generic mechanism, diversity, that provokes the emergence of global oscillations from individually quiescent elements in heterogeneous excitable media. This mechanism may be operating in the mammalian pancreas, where excitable beta cells, quiescent when isolated, are found to oscillate when coupled despite the absence of a pacemaker region.Comment: See home page http://lec.ugr.es/~julya

Manifestation of Chaos in Real Complex Systems: Case of Parkinson's Disease

In this chapter we present a new approach to the study of manifestations of chaos in real complex system. Recently we have achieved the following result. In real complex systems the informational measure of chaotic chatacter (IMC) can serve as a reliable quantitative estimation of the state of a complex system and help to estimate the deviation of this state from its normal condition. As the IMC we suggest the statistical spectrum of the non-Markovity parameter (NMP) and its frequency behavior. Our preliminary studies of real complex systems in cardiology, neurophysiology and seismology have shown that the NMP has diverse frequency dependence. It testifies to the competition between Markovian and non-Markovian, random and regular processes and makes a crossover from one relaxation scenario to the other possible. On this basis we can formulate the new concept in the study of the manifestation of chaoticity. We suggest the statistical theory of discrete non-Markov stochastic processes to calculate the NMP and the quantitative evaluation of the IMC in real complex systems. With the help of the IMC we have found out the evident manifestation of chaosity in a normal (healthy) state of the studied system, its sharp reduction in the period of crises, catastrophes and various human diseases. It means that one can appreciably improve the state of a patient (of any system) by increasing the IMC of the studied live system. The given observation creates a reliable basis for predicting crises and catastrophes, as well as for diagnosing and treating various human diseases, Parkinson's disease in particular.Comment: 20 pages, 8 figures, 3 tables. To be published in "The Logistic Map and the Route to Chaos: From the Beginnings to the Modern Applications", eds. by M. Ausloos, M. Dirickx, pp. 175-196, Springer-Verlag, Berlin (2006

Impurity-induced stabilization of solitons in arrays of parametrically driven nonlinear oscillators

Chains of parametrically driven, damped pendula are known to support soliton-like clusters of in-phase motion which become unstable and seed spatiotemporal chaos for sufficiently large driving amplitudes. We show that the pinning of the soliton on a "long" impurity (a longer pendulum) expands dramatically its stability region whereas "short" defects simply repel solitons producing effective partition of the chain. We also show that defects may spontaneously nucleate solitons.Comment: 4 pages in RevTeX; 7 figures in ps forma

Two and three-dimensional oscillons in nonlinear Faraday resonance

We study 2D and 3D localised oscillating patterns in a simple model system exhibiting nonlinear Faraday resonance. The corresponding amplitude equation is shown to have exact soliton solutions which are found to be always unstable in 3D. On the contrary, the 2D solitons are shown to be stable in a certain parameter range; hence the damping and parametric driving are capable of suppressing the nonlinear blowup and dispersive decay of solitons in two dimensions. The negative feedback loop occurs via the enslaving of the soliton's phase, coupled to the driver, to its amplitude and width.Comment: 4 pages; 1 figur

Depinning of kinks in a Josephson-junction ratchet array

We have measured the depinning of trapped kinks in a ratchet potential using a fabricated circular array of Josephson junctions. Our ratchet system consists of a parallel array of junctions with alternating cell inductances and junctions areas. We have compared this ratchet array with other circular arrays. We find experimentally and numerically that the depinning current depends on the direction of the applied current in our ratchet ring. We also find other properties of the depinning current versus applied field, such as a long period and a lack of reflection symmetry, which we can explain analytically.Comment: to be published in PR

Dynamical phase diagram of the dc-driven underdamped Frenkel-Kontorova chain

Multistep dynamical phase transition from the locked to the running state of atoms in response to a dc external force is studied by MD simulations of the generalized Frenkel-Kontorova model in the underdamped limit. We show that the hierarchy of transition recently reported [Braun et al, Phys. Rev. Lett. 78, 1295 (1997)] strongly depends on the value of the friction constant. A simple phenomenological explanation for the friction dependence of the various critical forces separating intermediate regimes is given.Comment: 12 Revtex Pages, 4 EPS figure

Small-world networks: Evidence for a crossover picture

Watts and Strogatz [Nature 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder $p$ in the links, the network behaves as a small-world. Here, we test the hypothesis that the appearance of small-world behavior is not a phase-transition but a crossover phenomenon which depends both on the network size $n$ and on the degree of disorder $p$. We propose that the average distance $\ell$ between any two vertices of the network is a scaling function of $n / n^*$. The crossover size $n^*$ above which the network behaves as a small-world is shown to scale as $n^*(p \ll 1) \sim p^{-\tau}$ with $\tau \approx 2/3$.Comment: 5 pages, 5 postscript figures (1 in color), Latex/Revtex/multicols/epsf. Accepted for publication in Physical Review Letter