Analysis of stability and bifurcations of limit cycles in Chua's circuit through the harmonic balance approach

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS: PART

Equilibrium analysis of cellular neural networks

Cellular neural networks are dynamical systems, described by a large set of coupled nonlinear differential equations. The equilibrium point analysis is an important step for understanding the global dynamics and for providing design rules. We yield a set of sufficient conditions (and a simple algorithm for checking them) ensuring the existence of at least one stable equilibrium point. Such conditions give rise to simple constraints, that extend the class of CNN, for which the existence of a stable equilibrium point is rigorously proved. In addition, they are suitable for design and easy to check, because they are directly expressed in term of the template elements

Qualitative analysis of the dynamics of the time delayed Chua's circuit

IEEE TRANS. CIRCUITS SYST.

Radio Loud AGNs are Mergers

We measure the merger fraction of Type 2 radio-loud and radio-quiet active galactic nuclei at z>1 using new samples. The objects have HST images taken with WFC3 in the IR channel. These samples are compared to the 3CR sample of radio galaxies at z>1 and to a sample of non-active galaxies. We also consider lower redshift radio galaxies with HST observations and previous generation instruments (NICMOS and WFPC2). The full sample spans an unprecedented range in both redshift and AGN luminosity. We perform statistical tests to determine whether the different samples are differently associated with mergers. We find that all (92%) radio-loud galaxies at z>1 are associated with recent or ongoing merger events. Among the radio-loud population there is no evidence for any dependence of the merger fraction on either redshift or AGN power. For the matched radio-quiet samples, only 38% are merging systems. The merger fraction for the sample of non-active galaxies at z>1 is indistinguishable from radio-quiet objects. This is strong evidence that mergers are the triggering mechanism for the radio-loud AGN phenomenon and the launching of relativistic jets from supermassive black holes. We speculate that major BH-BH mergers play a major role in spinning up the central supermassive black holes in these objects.Comment: 16 pages, 6 figures, accepted for publication in the Ap

Array of Josephson junctions with a non-sinusoidal current-phase relation as a model of the resistive transition of unconventional superconductors

An array of resistively and capacitively shunted Josephson junctions with nonsinusoidal current-phase relation is considered for modelling the transition in high-T$_c$ superconductors. The emergence of higher harmonics, besides the simple sinusoid $I_{c}\sin\phi$, is expected for dominant \emph{d}-wave symmetry of the Cooper pairs, random distribution of potential drops, dirty grains, or nonstationary conditions. We show that additional cosine and sine terms act respectively by modulating the global resistance and by changing the Josephson coupling of the mixed superconductive-normal states. First, the approach is applied to simulate the transition in disordered granular superconductors with the weak-links characterized by nonsinusoidal current-phase relation. In granular superconductors, the emergence of higher-order harmonics affects the slope of the transition. Then, arrays of intrinsic Josephson junctions, naturally formed by the CuO$_2$ planes in cuprates, are considered. The critical temperature suppression, observed at values of hole doping close to $p=1/8$, is investigated. Such suppression, related to the sign change and modulation of the Josephson coupling across the array, is quantified in terms of the intensities of the first and second sinusoids of the current-phase relation. Applications are envisaged for the design and control of quantum devices based on stacks of intrinsic Josephson junctions.Comment: Added: comparison with experiments; reference

LOCALIZED OSCILLATIONS IN DIFFUSIVELY COUPLED CYCLIC NEGATIVE FEEDBACK SYSTEMS

Oscillations in networks composed of Cyclic Negative Feedback systems (CNF systems) are widely used to mimic many periodic phenomena occurring in systems biology. In particular, the possible coexistence of different attractors permits to suitably describe the differentiating processes arising in living cells. The aim of the manuscript is to characterize, through a spec- tral based technique, the complex global dynamical behaviors emerging in arrays of diffusively coupled CNF systems

A dynamic system approach to spiking second order memristor networks

Second order memristors are two terminal devices that present a conductance depending on two orders of variables, namely the geometric parameters and the internal temperature. They have shown to be able to mimic some specific features of neuron synapses, specifically Spike-Timing-Dependent-Plasticity (STDP), and consequently to be good candidates for neuromor- phic computing. In particular, memristor crossbar structures appear to be suitable for implementing locally competitive algorithms and for tackling classification problems by exploiting temporal learning techniques. On the other hand, neuromorphic studies and experiments have revealed the existence of differ- ent kinds of plasticity and have shown the effect of calcium concentration on synaptic changes. Computational studies have investigated the behavior of spiking networks in the context of supervised, unsupervised, and reinforcement learning. In this paper, we first derive a simplified, almost analytical, model of a second-order memristor, only involving two variables, the mem- conductance, and the temperature, directly attributable to the synaptic efficacy and to the calcium concentration. Then we study in detail the response of a single memristive synapse to the most relevant plasticity models, including cycles of spike pairs, triplets, and quadruplets at different frequencies. Finally, we accurately characterize memristor spiking networks as discrete nonlinear dynamic systems, with mem-conductances as state variables and pre and postsynaptic spikes as inputs and outputs, respectively. The result shows that the model developed in this manuscript can explain and accurately reproduce a significant portion of observed synaptic behaviors, including those not captured by classical spike pair-based STDP models. Furthermore, under such an approach, the global dynamic behavior of memristor networks and the related learning mechanisms can be deeply analyzed by employing advanced nonlinear dynamic techniques

Resistive transition in granular disordered high Tc superconductors: a numerical study

The resistive transition of granular high-Tc superconductors, characterized by either weak (YBCO-like) or strong (MgB2-like) links, occurs through a series of avalanche-type current-density rearrangements. These rearrangements correspond to the creation of resistive layers, crossing the whole specimen approximately orthogonal to the current-density direction, due to the simultaneous transition of a large number of weak links or grains. The present work shows that exact solution of the Kirchhoff equations for strongly and weakly linked networks of nonlinear resistors, with Josephson-junction characteristics, yield the subsequent formation of resistive layers within the superconductive matrix as temperature increases. Furthermore, the voltage noise observed at the transition is related to the resistive layer formation process. The noise intensity is estimated from the superposition of voltage drop elementary events related to the subsequent resistive layers. At the end of the transition, the layers mix up, the step amplitude decreases, and the resistance curve smooths. This results in the suppression of noise, as experimentally found. Remarkably, a scaling law for the noise intensity with the network size is argued. It allows us to extend the results to networks with arbitrary size and, thus, to real specimen