Synchronized state of coupled dynamics on time-varying networks

We consider synchronization properties of coupled dynamics on time-varying networks and the corresponding time-average network. We find that if the different Laplacians corresponding to the time-varying networks commute with each other then the stability of the synchronized state for both the time-varying and the time-average topologies are approximately the same. On the other hand for noncommuting Laplacians the stability of the synchronized state for the time-varying topology is in general better than the time-average topology.     

Delay-induced cluster patterns in coupled Cayley tree networks

We study effects of delay in diffusively coupled logistic maps on the Cayley tree networks. We find that smaller coupling values exhibit sensitiveness to value of delay, and lead to different cluster patterns of self-organized and driven types. Whereas larger coupling strengths exhibit robustness against change in delay values, and lead to stable driven clusters comprising nodes from last generation of the Cayley tree. Furthermore, introduction of delay exhibits suppression as well as enhancement of synchronization depending upon coupling strength values. To the end we discuss the importance of results to understand conflicts and cooperations observed in family business.     

Synchronized family dynamics in globally coupled maps

The dynamics of a globally coupled, logistic map lattice is explored over a parameter plane consisting of the coupling strength, varepsilon, and the map parameter, a. By considering simple periodic orbits of relatively small lattices, and then an extensive set of initial-value calculations, the phenomenology of solutions over the parameter plane is broadly classified. The lattice possesses many stable solutions, except for sufficiently large coupling strengths, where the lattice elements always synchronize, and for small map parameter, where only simple fixed points are found. For smaller varepsilon and larger a, there is a portion of the parameter plane in which chaotic, asynchronous lattices are found. Over much of the parameter plane, lattices converge to states in which the maps are partitioned into a number of synchronized families. The dynamics and stability of two-family states (solutions partitioned into two families) are explored in detail. (c) 1999 American Institute of Physics.     

Active transport and cluster formation on 2D networks

We introduce a model for active transport on inhomogeneous networks embedded in a diffusive environment which is motivated by vesicular transport on actin filaments. In the presence of a hard-core interaction, particle clusters are observed that exhibit an algebraically decaying distribution in a large parameter regime, indicating the existence of clusters on all scales. The scale-free behavior can be understood by a mechanism promoting preferential attachment of particles to large clusters. The results are compared with a diffusion-limited aggregation model and active transport on a regular network. For both models we observe aggregation of particles to clusters which are characterized by a finite size scale if the relevant time scales and particle densities are considered.     

Relativistic coupled cluster method

Relativistic coupled cluster method (CCM) is applied to compute the low lying excited and ion states of strontium and ytterbium atom. The resulting excitation and ionization energies are in excellent agreement with experimental data and with other correlated calculations. The nuclear magnetic dipole hyperfine constants (A) and electric quadrupole hyperfine constants (B) of excited states are also evaluated and are in accord with experiment. We further address the basis set dependency of the computed properties.     

Stochastic coupled cluster theory

We describe a stochastic coupled cluster theory which represents excitation amplitudes as discrete excitors in the space of excitation amplitudes. Reexpressing the coupled cluster (CC) equations as the dynamics of excitors in this space, we show that a simple set of rules suffices to evolve a distribution of excitors to sample the CC solution and correctly evaluate the CC energy. These rules are not truncation specific and this method can calculate CC solutions to an arbitrary level of truncation. We present results of calculation on the neon atom, and nitrogen and water molecules showing the ability to recover both truncated and full CC results.     

Synchronized oscillations in a system of two coupled van-der-pol-duffing oscillators

The results of analysis of the periodic solutions obtained within the framework of complete and truncated equations for a system of identical Van-der-Pol-Duffing oscillators with nonlinear coupling are compared. This work was presented at the Summer Workshop “Dynamic Days” (Nizhny Novgorod, June 30–July 2, 1998). Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 12, pp. 1531–1536, December, 1998.     

Silicon cluster formation in the laser ablation of SiO at 308 nm

Neutral silicon cluster formation in the laser (308 nm) ablation of silicon monoxide was investigated through the analysis of composition and dynamics of the ablation plume under different laser fluence conditions. The neutral species were ionized by a second laser (193 nm) and the positionized species detected by TOF-MS (time-of-flight mass spectrometry). At low laser fluences, plume composition is dominated by SiO; above 0.6 J/cm² Si, SiO and Si₂ have comparable intensity and Si_n (n≤7) clusters are observed. Flow velocities and temperatures of the ejected species are nearly mass-independent, indicating that the plume dynamics are close to the strong expansion limit, implying a collisional regime. Through the relation between the estimated values of terminal flow velocity and surface temperature, u_T²∝T_S, it is found that, at low laser fluences, the surface temperature increases linearly with laser fluence, whereas, at the laser fluence at which Si_n clusters are observed, the increase of temperature is below the linear dependence. The population distribution of the ejected Si_n provides some indication of a formation mechanism based on condensation. Analogies between the ablation behavior of silicon monoxide and silicon targets are considered. PACS 82.30.Nr; 81.05.Gc; 78.70.-g     

Analyzing cluster formation in adaptive networks of Kuramoto oscillators by means of integral signals

A numerical study of an adaptive network of coupled oscillators (Kuramoto oscillators) is performed. The problem of studying phase synchronization in networks by considering wavelet spectra of the integral signal and the evolution of the phase difference in clusters of the adaptive network is examined. The process behind the formation of phase clusters is analyzed using integral characteristics.     

Difference in formation of carbon cluster cations by laser ablation of graphene and graphene oxide

The distributions of positive carbon cluster ions produced by laser ablation of graphene (G) and graphene oxide (GO) are found to be quite different. Under a typical experimental condition, narrow distributions of even-numbered clusters from C60+ to C162+ were observed for G, and broad distributions including even-numbered clusters from C100+ to C400+ and odd-numbered clusters from C189+ to C395+ were observed for GO. The threshold of laser energy for G is lower than that of GO. Further results of collision-activated dissociation mass spectrometry indicate that the cluster ions generated from G are structurally similar but are different with those generated from GO or nanodiamonds. It is proposed that the experimentally observed difference can be attributed to the different mechanisms behind the process. A top-down mechanism including both direct transformation of G to fullerene and fragmentation of large-sized fullerenes is suggested for the generation of carbon cluster cations in the process of laser ablation of G. For GO, the experimental results are close to those of nanodiamonds and other materials reported previously and can be explained by the generally accepted bottom-up mechanism.     

Modelling conflicts with cluster dynamics in networks

We introduce cluster dynamical models of conflicts in which only the largest cluster can be involved in an action. This mimics the situations in which an attack is planned by a central body, and the largest attack force is used. We study the model in its annealed random graph version, on a fixed network, and on a network evolving through the actions. The sizes of actions are distributed with a power-law tail, however, the exponent is non-universal and depends on the frequency of actions and sparseness of the available connections between units. Allowing the network reconstruction over time in a self-organized manner, e.g., by adding the links based on previous liaisons between units, we find that the power-law exponent depends on the evolution time of the network. Its lower limit is given by the universal value 5/2, derived analytically for the case of random fragmentation processes. In the temporal patterns behind the size of actions we find long-range correlations in the time series of the number of clusters and the non-trivial distribution of time that a unit waits between two actions. In the case of an evolving network the distribution develops a power-law tail, indicating that through repeated actions, the system develops an internal structure with a hierarchy of units.     

Projective cluster synchronization in drive-response dynamical networks

In this paper, we study the projective cluster synchronization in a drive-response dynamical network with 1+N coupled partially linear chaotic systems. Because the scaling factors characterizing the dynamics of projective synchronization remain unpredictable, pinning control ideas are adopted to direct the different scaling factors onto the desired values. It is also shown that the projection cluster synchronization can be realized by controlling only one node in each cluster. Numerical simulations on the chaotic Lorenz system are illustrated to verify the theoretical results.     

Adaptive cluster synchronization in complex dynamical networks

Cluster synchronization is investigated in different complex dynamical networks. In this Letter, a novel adaptive strategy is proposed to make a complex dynamical network achieve cluster synchronization, where the adaptive strategy of one edge is adjusted only according to its local information. A sufficient condition about the global stability arbitrarily grouped of cluster synchronization is derived. Several numerical simulations show the effectiveness of the adaptive strategy.     

Synchronization on coupled dynamical networks

In this paper, partial synchronization (PaS) in networks of coupled chaotic oscillator systems and synchronization in sparsely coupled spatiotemporal systems are explored. For the PaS, we reveal that the existence of PaS patterns depends on the symmetry property of the network topology, while the emergence of the PaS pattern depends crucially on the stability of the corresponding solution. An analytical criterion in judging the stability of PaS state on a given network are proposed in terms of a comparison between the Lyapunov exponent spectrum of the PaS manifold and that of the transversal manifold. The competition and selections of the PaS patterns induced by the presence of multiple topological symmetries of the network are studied in terms of the criterion. The phase diagram in distinguishing the synchronous and the asynchronous states is given. The criterion in judging PaS is further applied to the study of synchronization of two sparsely coupled spatiotemporal chaotic systems. Different synchronization regimes are distinguished. The present study reveals the intrinsic collective bifurcation of coupled dynamical systems prior to the emergence of global synchronization.     

Pairwise decoherence in coupled spin qubit networks

Experiments involving phase coherent dynamics of networks of spins, such as echo experiments, will only work if decoherence can be suppressed. We show here, by analyzing the particular example of a crystalline network of Fe8 molecules, that most decoherence typically comes from pairwise interactions (particularly dipolar interactions) between the spins, which cause "correlated errors." However, at very low T these are strongly suppressed. These results have important implications for the design of quantum information processing systems using electronic spins.     

Detecting synchronization in coupled stochastic ecosystem networks

Instantaneous phase difference, synchronization index and mutual information are considered in order to detect phase transitions, collective behaviours and synchronization phenomena that emerge for different levels of diffusive and reactive activity in stochastic networks. The network under investigation is a spatial 2D lattice which serves as a substrate for Lotka-Volterra dynamics with 3rd order nonlinearities. Kinetic Monte Carlo simulations demonstrate that the system spontaneously organizes into a number of asynchronous local oscillators, when only nearest neighbour interactions are considered. In contrast, the oscillators can be correlated, phase synchronized and completely synchronized when introducing different interactivity rules (diffusive or reactive) for nearby and distant species. The quantitative measures of synchronization show that long distance diffusion coupling induces phase synchronization after a well defined transition point, while long distance reaction coupling induces smeared phase synchronization.     

Self-action of laser radiation in cluster plasma

We have analytically and numerically studied the self-action dynamics of laser radiation in a plasma with ionized gas clusters. Based on the simplified model of a cluster in the form of a superposition of two charged (electron and ion) bunches, we analyze the nonlinearity mechanisms. We refine the electrodynamic cluster model by the molecular dynamics method. The polarization behavior of the plasma bunch in the main part of the laser pulse is shown to be the same as that in the simplified model. We investigate the self-action dynamics of laser radiation under conditions when the nonlinearity of the stratified medium is determined by the anharmonicity of the electron motion in the cluster, while the group velocity dispersion is determined by both the background plasma and the ionized clusters. Since the characteristic field for the electron nonlinearity depends strongly on the cluster size, the peculiarities of the self-action dynamics result from plasma bunch expansion. The spatiotemporal evolution of the wave field is shown to be accompanied by pulse self-compression near the trailing edge.     

耦合小世界神经网络的随机共振

噪声广泛存在于生物神经系统中,对系统功能具有重要作用.采用神经元二维映射模型构建一个复杂神经网络,由多个小世界子网络构成,研究了Gaussian白噪声诱导的随机共振现象.研究发现,只有合适的噪声强度才能使神经网络对输入刺激信号的频率响应达到峰值.另外,网络结构对系统随机共振特性有重要影响.在固定的耦合强度下,存在一个最优的局部小世界子网络结构,使得整个系统的频率响应最佳.     

Self-focusing of laser radiation in cluster plasma

The self-focusing of laser radiation in plasma with ionized gaseous clusters is studied both analytically and numerically. An electrodynamic model is proposed for cluster plasma in a field of ultrashort laser pulse. The radiation self-action dynamics are studied using the equation for wave-field envelope with allowance for the electronic nonlinearity of the expanded plasma bunches and the group-velocity dispersion in a nanodispersive medium. It is shown that, for a laser power exceeding the self-focusing critical power, the wave-field self-compression occurs in a medium with dispersion of any type (normal, anomalous, or combined). Due to the strong dependence of the characteristic nonlinear field on the size of ionized cluster, the corresponding processes develop faster than in a homogeneous medium and give rise to the ultrashort pulses.