Context. Evidence supports the idea that asteroids are rubble piles, that is, gravitational aggregates of loosely consolidated material. This makes their dynamics subject not only to the complex N-body gravitational interactions between its constituents, but also to the laws of granular mechanics, which is one of the main unsolved problems in physics. Aims. We aim to develop a new method to identify dynamical transitions and predict qualitative behavior in the granular N-body problem, in which the dynamics of individual bodies are driven both by mutual gravity, contact and collision interactions. Methods. The method has its foundation in the combination of two elements: a granular N-body simulation code that can resolve the dynamics of granular fragments to particle-scale precision, and a theoretical framework that can decode the nature of particle-scale dynamics and their transitions by means of ad hoc indicators. Results. We present here a proof-of-concept of the method, with application to the spinning rubble-pile asteroid problem. We investigate the density-spin parameter space and demonstrate that the approach can identify the breakup limit and reshape region for spinning rubble-pile aggregates. Conclusions. We provide the performance of several ad hoc indicators and discuss whether they are suitable for identifying and predicting the features of the dynamical problem.

We report the activation of optomechanical chaotic oscillations and chaos transfer from a strong pump to a very weak probe in microbubble resonators, both signals follow the same route to chaos.

The chaotic advection of fluid particle pairs is investigated though a low-order model of two-dimensional magnetohydrodynamic (MHD), where only five nonlinearly interacting modes are retained. The model is inthrinsically inhomogeneous and anisotropic because of the influence of large-scale fluctuations. Therefore, even though dynamically chaotic, the fields are unable to form the typical scaling laws of fully developed turbulence. Results show that a super-ballistic dynamics, reminiscent of the Richardson law of particle-pairs diffusion in turbulent flows, is robustly obtained using the truncated model. Indeed, even in the strongly reduced truncation presented here, particle diffusion in MHD turbulence has the same laws as the separation of velocity of particle pairs. The inherent anisotropy only affects the scaling of diffusivity, by enhancing the diffusion properties along one direction for small time-scales. Finally, when further anisotropy is introduced in the system through Alfvén waves, fluid particles are trapped by these, and super-ballistic diffusion is replaced by Brownian-like diffusion. On the other hand, when the magnetic field is removed, the kinetic counterpart of the model does not show super-ballistic dynamics.

Analysis of Lagrangian Coherent Structures (LCSs) has been shown to be a valid mathematical approach to explain the formation of transport barriers in magnetized plasmas. Such LCSs, borrowed from fluid dynamics theory, can be considered as the hidden skeleton of the system and can be used for studying a wide spectrum of transport mechanisms, even in plasmas. An LCS can be considered as a generalization for a finite time interval and for a general dynamical system of what manifolds are for Hamiltonian systems. In this paper, we demonstrate that such structures can be particularly useful for underlying the hidden paths governing the motion of magnetic field lines in chaotic magnetic fields. To perform such an analysis, we developed a numerical tool able to detect LCSs for a general dynamical system. The tool is able to deal with general coordinate systems and it is shown to match with other techniques already used to analyse chaotic magnetic fields, e.g. connection length. After the description of the computational tool, we focus on the heat transport equation and the comparison between temperature profile and topology of the LCSs. We provide evidence that numerical simulations are able to reproduce the temperature profiles similar to those observed in reversed field pinch experiments and that our tool successfully predicts the location of temperature gradients. The results suggest that, inside the chaotic region, the field-lines motion is far from stochastic and that the presence of hidden patterns allows the development of high temperature gradients.

We report on the experimental analysis of parametrical optomechanical oscillations and nonlinear frequency generation in hollow phoxonic whispering gallery mode resonators. Both phenomena can be enchanced or suppressed and showed chaotic behavior.

Anytime-reliable communication systems are needed in contexts where the property of vanishing error probability with time is critical. This is the case of unstable real-time systems that have to be controlled through the transmission and processing of remotely sensed data. The most successful anytime-reliable transmission systems developed so far are based on channel codes and channel coding theory. In this paper, another focus is proposed, placing the stress on the waveform level rather than just on the coding level. This alleviates the coding and decoding complexity problems faced by other proposals. To this purpose, chaos theory is successfully exploited in order to design two different anytime-reliable alternatives. The anytime-reliability property is formally demonstrated in each case for the AWGN channel, under given conditions. The simulation results shown validate the theoretical developments, and demonstrate that these systems can achieve anytime reliability with affordable resource expenditure.

We propose an electronic implementation to record Poincar& x00E9; sections of dynamical systems exhibiting chaos. Poincar& x00E9; sections are obtained by sampling and holding the maxima of a sequence of pulses of a chaotic relaxation oscillator versus the same temporal sequence shifted by one unit. By using these sections we are able to detail the transition to chaos via torus breakdown.

The magnetic topology of the stochastic edge of a helical reversed-field pinch, with helicity m/n, shows to be deeply influenced by higher harmonics (m +/- 1)/n, with the same n, due to toroidal coupling. As a consequence, by measuring kinetic quantities in a particular theta, phi location, one can incur in substantial errors or mis-interpretations of the kinetic plasma response: only a full 3D coverage of theta, phi angles can reveal the real topology of the plasma. This can be a caveat for MP application in tokamaks, because it shows that toroidal and poloidal sidebands, though smaller than the base mode by a factor similar to epsilon = a/R, can have a sizable effect on the kinetic response of the edge plasma, and thus on related issues (for example, ELM stabilization and suppression).

Review of fundamental concepts concerning the study of transport, mixing and dispersion properties in nonlinear flows from a dynamical system perspective.

Numerical simulations carried out over the past decade suggest that the orbits of the Global Navigation Satellite Systems are unstable, resulting in an apparent chaotic growth of the eccentricity. Here, we show that the irregular and haphazard character of these orbits reflects a similar irregularity in the orbits of many celestial bodies in our Solar system. We find that secular resonances, involving linear combinations of the frequencies of nodal and apsidal precession and the rate of regression of lunar nodes, occur in profusion so that the phase space is threaded by a devious stochastic web. As in all cases in the Solar system, chaos ensues where resonances overlap. These results may be significant for the analysis of disposal strategies for the four constellations in this precarious region of space.

We investigate the polarization dynamics in a quasi-isotropic CO2 laser emitting on the TEM01* mode subjected to an optical feedback. We observe a complex dynamics in which spatial mode and polarization competition are involved. The observed dynamics is well reproduced by a model that discriminates between the intrinsic asymmetry due to the kinetic coupling of molecules with different angular momenta and the anisotropy induced by the polarization feedback. We observe various dynamical regimes including chaotic dynamics and show that feedback changes these states from regular to chaotic and vice versa. Finally, the possible applications to polarization coding are discussed.

When an ambiguous stimulus is observed, our perception undergoes dynamical changes between two states, a situation extensively explored in association with the Necker cube. Such phenomenon refers to bistable perception. Here, we present a model neural network composed of forced FitzHugh-Nagumo neurons, implemented also experimentally in an electronic circuit. We show, that under a particular coupling configuration, the neural network exhibit bistability between two configurations of clusters. Each cluster composed of two neurons undergoes independent chaotic spiking dynamics. As an appropriate external perturbation is applied to the system, the network undergoes changes in the clusters configuration, involving different neurons at each time. We hypothesize that the winning cluster of neurons, responsible for perception, is that exhibiting higher mean frequency. The clusters features may contribute to an increase of local field potential in the neural network.

The idea of predicting the future from the knowledge of the past is quite natural, even when dealing with systems whose equations of motion are not known. This long-standing issue is revisited in the light of modern ergodic theory of dynamical systems and becomes particularly interesting from a pedagogical perspective due to its close link with Poincare's recurrence. Using such a connection, a very general result of ergodic theory-Kac's lemma-can be used to establish the intrinsic limitations to the possibility of predicting the future from the past. In spite of a naive expectation, predictability is hindered more by the effective number of degrees of freedom of a system than by the presence of chaos. If the effective number of degrees of freedom becomes large enough, whether the system is chaotic or not, predictions turn out to be practically impossible. The discussion of these issues is illustrated with the help of the numerical study of simple models.

In this article, we investigate the role of connectivity in promoting coherent activity in excitatory neural networks. In particular, we would like to understand if the onset of collective oscillations can be related to a minimal average connectivity and how this critical connectivity depends on the number of neurons in the networks. For these purposes, we consider an excitatory random network of leaky integrate-and-fire pulse coupled neurons. The neurons are connected as in a directed Erdos-Renyi graph with average connectivity < k > scaling as a power law with the number of neurons in the network. The scaling is controlled by a parameter gamma, which allows to pass from massively connected to sparse networks and therefore to modify the topology of the system. At a macroscopic level, we observe two distinct dynamical phases: an asynchronous state corresponding to a desynchronized dynamics of the neurons and a regime of partial synchronization (PS) associated with a coherent periodic activity of the network. At low connectivity, the system is in an asynchronous state, while PS emerges above a certain critical average connectivity < k >(c). For sufficiently large networks, < k >(c) saturates to a constant value suggesting that a minimal average connectivity is sufficient to observe coherent activity in systems of any size irrespectively of the kind of considered network: sparse or massively connected. However, this value depends on the nature of the synapses: reliable or unreliable. For unreliable synapses, the critical value required to observe the onset of macroscopic behaviors is noticeably smaller than for reliable synaptic transmission. Due to the disorder present in the system, for finite number of neurons we have inhomogeneities in the neuronal behaviors, inducing a weak form of chaos, which vanishes in the thermodynamic limit. In such a limit, the disordered systems exhibit regular (non chaotic) dynamics and their properties correspond to that of a homogeneous fully connected network for any gamma-value. Apart for the peculiar exception of sparse networks, which remain intrinsically inhomogeneous at any system size.

The transitional phase from local to global chaos in the magnetic field of a reconnecting current layer is investigated. The identification of the ridges in the field of the finite time Lyapunov exponent as barriers to the field line motion is carried out adopting the technique of field line spectroscopy to analyze the radial position of a field line while it winds its way through partial stochastic layers and to compare the frequencies of the field line motion with the corresponding frequencies of the distinguished hyperbolic field lines that are the nonlinear generalizations of linear X-lines.

The transitional phase from local to global chaos in the magnetic field of a reconnecting current layer is investigated. Regions where the magnetic field is stochastic exist next to regions where the field is more regular. In regions between stochastic layers and between a stochastic layer and an island structure, the field of the finite time Lyapunov exponent (FTLE) shows a structure with ridges. These ridges, which are special gradient lines that are transverse to the direction of minimum curvature of this field, are approximate Lagrangian coherent structures (LCS) that act as barriers for the transport of field lines.

We present a multi-frequency phase control able to preserve a periodic behaviour within a chaotic window as well as to re-excite chaotic behaviour when it is destroyed. The validity of this non feedback method has been shown in the cobweb model with adaptive price expectations as well as in the quadratic map near an interior crisis. A crucial role is played by the phase of the applied periodic perturbations

We report on experimental evidence of generation and control of low spiking events in a semiconductor laser. An experiment has been carried on a semiconductor laser with an electro-optic feedback, set in a parameter range where chaos occurs. The feedback is modulated by 1 kHz and 10 kHz, frequencies, 50mV amplitudes. The dependence of the injected current on the feedback fraction is observed.

Recent developments in different interdisciplinary scientific areas (fractal geometry, information theory, analysis of complex and dissipative systems, emergence of auto-organization, chaos theory, and cellular automata) are creating new ways of thinking about Nature. These studies have revealed that fractal-chaos, at the border of the phase transition between order and chaos, is everywhere. Maps and clocks based on fractal layers of metabolic hypercycles might be used by living organisms to maintain their homodynamic equilibrium and biodiversity at different levels. The understanding of the dynamics of complex biological systems is very important to highlight the mechanisms of many physiological, evolutionary and ecological processes.