Fixed Coupling Strength Research Articles

Exponential synchronization of complex delayed dynamical networks via pinning periodically intermittent control

The problem of synchronization for a class of complex delayed dynamical networks via pinning periodically intermittent control is considered in this Letter. Some novel and useful exponential synchronization criteria are obtained by utilizing the methods which are different from the techniques employed in the existing works, and the derived results are less conservative. Especially, the traditional assumptions on control width and time delays are released in our results. Moreover, a pinning scheme deciding what nodes should be chosen as pinned candidates and how many nodes are needed to be pinned for a fixed coupling strength is provided. A Barabási–Albert network example is finally given to illustrate the effectiveness of the theoretical results.

Taming desynchronized bursting with delays in the Macaque cortical network

Inhibitory coupled bursting Hindmarsh—Rose neurons are considered as constitutive units of the Macaque cortical network. In the absence of information transmission delay the bursting activity is desynchronized, giving rise to spatiotemporally disordered dynamics. This paper shows that the introduction of finite delays can lead to the synchronization of bursting and thus to the emergence of coherent propagating fronts of excitation in the space-time domain. Moreover, it shows that the type of synchronous bursting is uniquely determined by the delay length, with the transitions from one type to the other occurring in a step-like manner depending on the delay. Interestingly, as the delay is tuned close to the transition points, the synchronization deteriorates, which implies the coexistence of different bursting attractors. These phenomena can be observed by different but fixed coupling strengths, thus indicating a new role for information transmission delays in realistic neuronal networks.

Firing responses of bursting neurons with delayed feedback

Thalamic neurons, which play important roles in the genesis of rhythmic activities of the brain, show various bursting behaviors, particularly modulated by complex thalamocortical feedback via cortical neurons. As a first step to explore this complex neural system and focus on the effects of the feedback on the bursting behavior, a simple loop structure delayed in time and scaled by a coupling strength is added to a recent mean-field model of bursting neurons. Depending on the coupling strength and delay time, the modeled neurons show two distinct response patterns: one entrained to the unperturbed bursting frequency of the neurons and one entrained to the resonant frequency of the loop structure. Transitions between these two patterns are explored in the model's parameter space via extensive numerical simulations. It is found that at a fixed loop delay, there is a critical coupling strength at which the dominant response frequency switches from the unperturbed bursting frequency to the loop-induced one. Furthermore, alternating occurrence of these two response frequencies is observed when the delay varies at fixed coupling strength. The results demonstrate that bursting is coupled with feedback to yield new dynamics, which will provide insights into such effects in more complex neural systems.

Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics

This paper considers the global stability of controlling an uncertain complex network to a homogeneous trajectory of the uncoupled system by a local pinning control strategy. Several sufficient conditions are derived to guarantee the network synchronisation by investigating the relationship among pinning synchronisation, network topology, and coupling strength. Also, some fundamental and yet challenging problems in the pinning control of complex networks are discussed: (1) what nodes should be selected as pinned candidates? (2) How many nodes are needed to be pinned for a fixed coupling strength? Furthermore, an adaptive pinning control scheme is developed. In order to achieve synchronisation of an uncertain complex network, the adaptive tuning strategy of either the coupling strength or the control gain is utilised. As an illustrative example, a network with the Lorenz system as node self-dynamics is simulated to verify the efficacy of theoretical results.

On Pinning Synchronization of Directed and Undirected Complex Dynamical Networks

This paper presents some low-dimensional pinning criteria for global synchronization of both directed and undirected complex networks, and proposes specifically pinning schemes to select pinned nodes by investigating the relationship among pinning synchronization, network topology, and the coupling strength. The paper answers the challenging questions in pinning control of complex networks: 1) what sufficient conditions can guarantee global asymptotic stability of the pinning process; 2) what nodes should be chosen as pinned candidates; and 3) how many nodes are needed to be pinned for a fixed coupling strength? Furthermore, an adaptive pinning control scheme is developed to achieve synchronization of general complex networks. Numerical examples are given to verify our theoretical analysis.

Commensurate quantum oscillations in coupled qubits

We study the coupled-qubit oscillation driven by an oscillating field. When the period of the nonresonant mode is commensurate with that of the resonant mode of the Rabi oscillation, we show that the controlled-NOT (CNOT) gate operation can be demonstrated. For a weak coupling the CNOT gate operation is achievable by the commensurate oscillations, while for a sufficiently strong coupling it can be done for arbitrary parameter values. By finely tuning the amplitude of oscillating field it is shown that the high fidelity of the CNOT gate can be obtained for any fixed coupling strength and qubit energy gap in experiments.

Clausius inequality beyond the weak-coupling limit: The quantum Brownian oscillator

We consider a quantum linear oscillator coupled at an arbitrary strength to a bath at an arbitrary temperature. We find an exact closed expression for the oscillator density operator. This state is noncanonical but can be shown to be equivalent to that of an uncoupled linear oscillator at an effective temperature T*(eff) with an effective mass and an effective spring constant. We derive an effective Clausius inequality deltaQ*(eff)< or =T*(eff)dS , where deltaQ*(eff) is the heat exchanged between the effective (weakly coupled) oscillator and the bath, and S represents a thermal entropy of the effective oscillator, being identical to the von-Neumann entropy of the coupled oscillator. Using this inequality (for a cyclic process in terms of a variation of the coupling strength) we confirm the validity of the second law. For a fixed coupling strength this inequality can also be tested for a process in terms of a variation of either the oscillator mass or its spring constant. Then it is never violated. The properly defined Clausius inequality is thus more robust than assumed previously.

ENHANCEMENT OF STOCHASTIC RESONANCE IN SPATIALLY EXTENDED SYSTEMS BY MEANS OF DELAYED COUPLING

Stochastic resonance in a chain of coupled threshold elements driven by a spatiotemporal periodic signal and noise is studied. It is shown that stochastic resonance can be enhanced for a fixed coupling strength by introducing proper time delays in the coupling terms which balance the effect of the phase difference between the periodic signals at the input of the interacting elements. Hence, in spatially extended systems driven by spatiotemporal periodic signals, stochastic resonance can be controlled by a delayed coupling. This method of controlling stochastic resonance is robust against random perturbations of the periodicity of the input signal and of the individual time delays.

Synchronizability determined by coupling strengths and topology on complex networks

We investigate in depth the synchronization of coupled oscillators on top of complex networks with different degrees of heterogeneity within the context of the Kuramoto model. In a previous paper [Phys. Rev. Lett. 98, 034101 (2007)], we unveiled how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks. Here, we provide more evidence on this phenomenon, extending the previous work to networks that interpolate between homogeneous and heterogeneous topologies. We also introduce details of the path towards synchronization for the evolution of clustering in the synchronized patterns. Finally, we investigate the synchronization of networks with modular structure and conclude that, in these cases, local synchronization is first attained at the most internal level of organization of modules, progressively evolving to the outer levels as the coupling constant is increased. The present work introduces parameters that are proved to be useful for the characterization of synchronization phenomena in complex networks.

Synchronization in a network of model neurons

We study the spatiotemporal dynamics of a network of coupled chaotic maps modelling neuronal activity, under variation of coupling strength epsilon and degree of randomness in coupling p. We find that at high coupling strengths (epsilon>epsilonfixed) the unstable saddle point solution of the local chaotic maps gets stabilized. The range of coupling where this spatiotemporal fixed point gains stability is unchanged in the presence of randomness in the connections, namely epsilonfixed is invariant under changes in p. As coupling gets weaker (epsilon<epsilonfixed), the spatiotemporal fixed point loses stability, and one obtains chaos. In this regime, when the coupling connections are completely regular (p=0), the network becomes spatiotemporally chaotic. Interestingly however, in the presence of random links (p>0) one obtains spatial synchronization in the network. We find that this range of synchronized chaos increases exponentially with the fraction of random links in the network. Further, in the space of fixed coupling strengths, the synchronization transition occurs at a finite value of p, a scenario quite distinct from the many examples of synchronization transitions at p-->0. Further we show that the synchronization here is robust in the presence of parametric noise, namely in a network of nonidentical neuronal maps. Finally we check the generality of our observations in networks of neurons displaying both spiking and bursting dynamics.

Paths to Synchronization on Complex Networks

The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals or units has been intensively studied because of its ubiquity in the natural world. In this Letter, we show how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks, driving the process towards a certain global synchronization degree following different paths. The dependence of the dynamics on the coupling strength and on the topology is unveiled. This study provides a new perspective and tools to understand this emerging phenomena.

증폭된 광 귀환을 가자는 다중 전극 복소 결합 DFB 레이저에서 발생되는 self-pulsation 특성 해석

하나의 DFB 영역, 위상 조정 영역과 이득 영역으로 구성된 다중 전극 DFB 레이저의 pulsation 동작 특성을 살펴본다. Anti-phase (AP) complex-coupled (CC) DFB 구조를 사용한 경우가 in-phase CC DFB 구조나 index-coupled DFB 구조를 사용한 경우에 비하여 안정된 pulsation 동작이 발생하는 이득 영역과 위상 조정 영역의 전류 범위가 큼을 알 수 있다. AP CC DFB 구조를 사용한 경우 결합 세기가 커질수록, 이득 결합 계수가 커질수록 안정된 pulsation 동작이 발생하는 이득 영역의 전류 범위가 증가하고 pulsation 주파수의 튜닝 영역이 커짐을 볼 수 있다. 또한 위상 조정 영역의 위상 변화에 의한 pulsation주파수의 튜닝 영역도 커짐을 볼 수 있다. 고정된 결합 세기에서 DFB 영역의 길이가 증가할수록 pulsation 동작이 발생하는 위상 조정 영역과 이득 영역의 전류 범위가 증가하여 pulsation 주파수 튜닝 영역이 넓어짐을 볼 수 있다. We investigate the pulsation characteristics in a multi-section DFB laser which is composed of one DFB section, phase tuning section, and gain section. Multi-section DFB lasers with anti-phase (AP) complex-coupled (CC) DFB structure show wide current ranges of gain and phase tuning sections fer stable pulsations compared to those with in-phase CC DFB structure or index-coupled DFB structure. For multi-section DFB lasers with AP CC DFB structure, the current range of a gain section for stable pulsations increases and the tuning range of the pulsation frequency increases as a coupling strength or a gain coupling coefficient increases Also, the tuning range using the phase variation in a phase tuning section increases. For a fixed coupling strength, the current ranges of gain and phase tuning sections for stable pulsations increase and the tuning range of the pulsation frequency increases as the length of a DFB section increases.

Synchronization in fractional-order differential systems

An ω -symmetrically coupled system consisting of identical fractional-order differential systems including chaotic and non-chaotic systems is investigated in this paper. Such a coupled system has, in its synchronous state, a mode decomposition by which the linearized equation can be decomposed into motions transverse to and parallel to the synchronous manifold. Furthermore, the decomposition can induce a sufficient condition on synchronization of the overall system, which guarantees, if satisfied, that a group synchronization is achieved. Two typical numerical examples, fractional Brusselators and the fractional Rössler system, are used to verify the theoretical prediction. The theoretical analysis and numerical results show that the lower the order of the fractional system, the longer the time for achieving synchronization at a fixed coupling strength.

Arbitrarily perfect quantum communication using unmodulated spin chains, a collaborative approach

We shall consider a quantum communication channel constituted by two open spin chains with nearest neighbour interactions and fixed coupling strengths, connected to several users. Assuming that the users of this quantum data bus can apply simple gates on sites of the chain that they are connected to, we will see that it is possible to gain information on the position of the qubit during the transmission, and to use this information to accelerate the communication process. We will also see that performing frequent measurements on the system affects the dynamics of propagation of quantum information in an interesting way.

Dynamics of a Ring of Diffusively Coupled Lorenz Oscillators

We study the dynamics of a finite chain of diffusively coupled Lorenz oscillators with periodic boundary conditions. Such rings possess infinitely many fixed states, some of which are observed to be stable. It is shown that there exists a stable fixed state in arbitrarily large rings for a fixed coupling strength. This suggests that coherent behavior in networks of diffusively coupled systems may appear at a coupling strength that is independent of the size of the network.

Electronic correlations, electron-phonon interaction, and isotope effect in high-Tccuprates

Using a large-$N$ expansion we present and solve the linearized equation for the superconducting gap for a generalized $t\ensuremath{-}J$ model which also contains phonons within a Holstein model. Keeping all terms up to $O(1/N)$ the kernel of the gap equation consists of an electron-phonon part with self-energies and vertex functions renormalized by the interactions of the $t\ensuremath{-}J$ model, and a $t\ensuremath{-}J$ part unaffected by phonons. Considering first the electron-phonon part we find that the leading superconducting instability always occurs in the s-wave channel with a ${T}_{c}$ which is lower compared to that of noninteracting electrons, especially at large dopings. The corresponding isotope coefficient $\ensuremath{\beta}$ is larger than $1/2$ and increases with decreasing doping. Including also the $t\ensuremath{-}J$ part in the gap equation the leading ${T}_{c}$ has always d-wave symmetry with phonons giving a positive contribution to ${T}_{c}.$ $\ensuremath{\beta}$ is very small at optimal doping and increases towards the classical value $1/2$ with increasing doping similar as in several cuprates. Considered as a function of the phonon frequency ${\ensuremath{\omega}}_{0}$ at a fixed coupling strength $\ensuremath{\beta}$ increases monotonously from zero to about $1/2$ with increasing ${\ensuremath{\omega}}_{0}.$

Evanescent field coupling between a single-mode fiber and a planar waveguide with absorption or gain

A coupled-mode model is presented, which is capable of describing the light transfer between a single-mode fiber and a planar waveguide (PWG), taking into account the TE or the TM polarization of the PWG modes and an absorption or a gain into the PWG or the cover medium. Applying this model to the practical case of a coupler of limited length (both with distributed and fixed coupling strength) I show that the initially strongly asymmetric resonance curve of coupling broadens, becoming more and more symmetric as the absorption increases. When the PWG and/or the cover medium possesses a gain, a reverse resonance (with an amplified fiber power) appears next to the resonance minimum of the fiber power.

Elastic and inelastic scattering of 16O and 12C by 24Mg near the Coulomb barrier

Angular distributions for 16O + 24Mg and 12C + 24Mg elastic and inelastic (2 +, 1.37 MeV state in 24Mg) scattering have been measured at energies spanning the Coulomb barrier. Apart from the structure typical of strong destructive Coulomb-nuclear interference, the data exhibit some additional specific features. Coupled channel calculations were performed, along with DWBA calculations to analyse the data using fixed coupling strengths deduced from the results of Coulomb excitation work. The importance of higher-order effects such as reorientation, is demonstrated.

On a class of thirring models

A class of Thirring models self-coupled through a non-covariant current operator is investigated. It is shown that such a coupling will lead to physically meaningful results only at a fixed coupling strength. Furthermore, symmetry-breaking solutions of a kind to be specified in the text are permissible only at this particular coupling strength. The question of Goldstone zero-mass bosons is discussed.