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1.
The synchronisation of spiral patterns in a drive-response R6ssler system is studied. The existence of three types of synchronisation is revealed by inspecting the coupling parameter space. Two transient stages of phase synchronisation and partial synchronisation are observed in a comparatively weak feedback coupling parameter regime, whilst complete synchronisation of spirals is found with strong negative couplings. Detailed observations of the synchronous process, such as oscillatory frequencies, parameters mismatches and amplitude variations, etc, are investigated via numerical simulations. 相似文献
2.
This paper numerically investigates the order parameter and
synchronisation in the small world
connected FitzHugh--Nagumo excitable systems. The simulations show
that the order parameter continuously decreases with increasing d,
the quality of the synchronisation worsens for large noise
intensity. As the coupling intensity goes up, the quality of the
synchronisation worsens, and it finds that the larger rewiring
probability becomes the larger order parameter. It obtains the
complete phase diagram for a wide range of values of noise intensity
d and control parameter g. 相似文献
3.
Development and transition of spiral wave in the coupled Hindmarsh--Rose neurons in two-dimensional space 总被引:1,自引:0,他引:1 下载免费PDF全文
The dynamics and the transition of spiral waves in the coupled
Hindmarsh--Rose (H--R) neurons in two-dimensional space are
investigated in the paper. It is found that the spiral wave can be
induced and developed in the coupled HR neurons in two-dimensional
space, with appropriate initial values and a parameter region given.
However, the spiral wave could encounter instability when the
intensity of the external current reaches a threshold value of
1.945. The transition of spiral wave is found to be affected by
coupling intensity D and bifurcation parameter r. The spiral
wave becomes sparse as the coupling intensity increases, while the
spiral wave is eliminated and the whole neuronal system becomes
homogeneous as the bifurcation parameter increases to a certain
threshold value. Then the coupling action of the four sub-adjacent
neurons, which is described by coupling coefficient D’, is also
considered, and it is found that the spiral wave begins to breakup
due to the introduced coupling action from the sub-adjacent neurons
(or sites) and together with the coupling action of the
nearest-neighbour neurons, which is described by the coupling
intensity D. 相似文献
4.
Synchronisation and general dynamic symmetry of a vibrating system with two exciters rotating in opposite directions 下载免费PDF全文
We derive the non-dimensional coupling equation of two
exciters, including inertia coupling, stiffness coupling and load
coupling. The concept of general dynamic symmetry is proposed to
physically explain the synchronisation of the two exciters, which
stems from the load coupling that produces the torque of general
dynamic symmetry to force the phase difference between the two
exciters close to the angle of general dynamic symmetry. The
condition of implementing synchronisation is that the torque of
general dynamic symmetry is greater than the asymmetric torque of
the two motors. A general Lyapunov function is constructed to derive
the stability condition of synchronisation that the non-dimensional
inertia coupling matrix is positive definite and all its elements are
positive. Numeric results show that the structure of the vibrating
system can guarantee the stability of synchronisation of the two
exciters, and that the greater the distances between the
installation positions of the two exciters and the mass centre of
the vibrating system are, the stronger the ability of general
dynamic symmetry is. 相似文献
5.
Generalised synchronisation of spatiotemporal chaos using feedback control method and phase compression 下载免费PDF全文
Coupled map lattices are taken as examples to study the synchronisation of spatiotemporal chaotic systems. First, a generalised synchronisation of two coupled map lattices is realised through selecting an appropriate feedback function and appropriate range of feedback parameter. Based on this method we use the phase compression method to extend the range of the parameter. So, we integrate the feedback control method with the phase compression method to implement the generalised synchronisation and obtain an exact range of feedback parameter. This technique is simple to implement in practice. Numerical simulations show the effectiveness and the feasibility of the proposed program. 相似文献
6.
Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics 下载免费PDF全文
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. 相似文献
7.
Realization of a broadband terahertz wavelength-selective coupling based on five-core fibers 下载免费PDF全文
We propose a novel kind of wavelength-selective coupling for the terahertz range based on solid five-core fiber(FCF).The performances of coupling, propagation characteristics, and confinement loss properties are numerically investigated by using a full vector beam propagation method(BPM). Simulation results show that it is possible to realize a broadband wavelength-selective coupling. The coupling length can reach 1.913 cm, and the confinement loss is better than1.965×10-4cm-1. Furthermore, a parameter, the power difference, is defined, and it numerically demonstrates the working performance of the wavelength-selective coupler; that is, when the power difference is better than-15 dB, the frequency located in the range of 0.76 THz–1.00 THz is separated relatively well from the frequency of 0.3 THz. Finally, the effect of the structural parameter on the working performance of the coupler is also investigated. We show that the performance optimization is possible by appropriately tuning the core diameter, and the tunabilities of frequency and bandwidth are possible by appropriately tuning the pitch. The wavelength-selective coupler is of potential application for optical fiber sensing and communication in terahertz wavelength division multiplexer fields. 相似文献
8.
Existence and Stability of Compact-Like Discrete Breather in Discrete One-Dimensional Monatomic Chains 下载免费PDF全文
Compact-like discrete breathers in discrete one-dimensional monatomic chains are investigated by discussing a generalized discrete one-dimensional monatomic model. It is proven that compact-like discrete breathers exist not only in soft Ф^4 potential but also in hard Ф^4 potential and K4 chains. The measurements of compact-like discrete breathers' core in soft and hard Ф^4 potential are determined by coupling parameter K4, while the measurements of compact-like discrete breathers' core in K4 chains are not related to coupling parameter K4. The stabilities of compact-like discrete breathers correlate closely to coupling parameter K4 and the boundary condition of lattice. 相似文献
9.
This paper studies the two-electron total energy and the
energy of the electron--electron interaction by using a variational
method of Pekar type on the condition of electric--LO-phonon strong
coupling in a parabolic quantum dot. It considers the following
three cases: 1) two electrons are in the ground state; 2) one
electron is in the ground state, the other is in the first-excited state;
3) two electrons are in the first-excited state. The relations of
the two-electron total energy and the energy of the
electron--electron interaction on the Coulomb binding parameter, the
electron-LO-phonon coupling constant and the confinement length of
the quantum dot are derived in the three cases. 相似文献
10.
Existence and Stability of Two-Dimensional Compact-Like Discrete Breathers in Discrete Two-Dimensional Monatomic Square Lattices 下载免费PDF全文
Two-dimensional compact-like discrete breathers in discrete two-dimensional monatomic square lattices are investigated by discussing a generalized discrete two-dimensional monatomic model. It is proven that the two- dimensional compact-like discrete breathers exist not only in two-dimensional soft Φ4 potentials but also in hard two-dimensional Φ4 potentials and pure two-dimensional K4 lattices. The measurements of the two-dimensional compact-like discrete breather cores in soft and hard two-dimensional Φ4 potential are determined by coupling parameter K4, while those in pure two-dimensional K4 lattices have no coupling with parameter K4. The stabilities of the two-dimensional compact-like discrete breathers correlate closely to the coupling parameter K4 and the boundary condition of lattices. 相似文献
11.
R. Donner 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,63(3):349-361
Networks of interacting components are a class of complex systems that has attracted considerable interest over the last decades.
In particular, if the dynamics of the autonomous components is characterised by an oscillatory behaviour, different types
of synchronisation can be observed in dependence on the type and strength of interactions. In this contribution, we study
the transition from non-synchronised to synchronised phase dynamics in complex networks. The most common approach to quantify
the degree of phase synchronisation in such systems is the consideration of measures of phase coherence which are averaged
over all pairs of interacting components. However, this approach implicitly assumes a spatially homogeneous synchronisation process,
which is typically not present in complex networks. As a potential alternative, two novel methods of multivariate phase synchronisation analysis are considered: synchronisation cluster analysis (SCA) and the linear variance decay (LVD)
dimension method. The strengths and weaknesses of the traditional as well as both new approaches are briefly illustrated for
a Kuramoto model with long-range coupling. As a practical application, we study how spatial heterogeneity influences the transition
to phase synchronisation in traffic networks where intersecting material flows are subjected to a self-organised decentralised
control. We find that the network performance and the degree of phase synchronisation are closely related to each other and
decrease significantly in the case of structural heterogeneities. The influences of the different parameters of our control
approach on the synchronisation process are systematically studied, yielding a sequence of Arnold tongues which correspond
to different locking modes. 相似文献
12.
We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function, we investigate the stability of the zero-lag synchronised dynamics of the network nodes and its dependence on the two coupling parameters, namely the coupling strength and delay time. Unlike in the FitzHugh-Nagumo model (a model for type-II excitability), there are parameter ranges where the stability of synchronisation depends on the coupling strength and delay time. One important implication of these results is that there exist complex networks for which the adding of inhibitory links in a small-world fashion may not only lead to a loss of stable synchronisation, but may also restabilise synchronisation or introduce multiple transitions between synchronisation and desynchronisation. To underline the scope of our results, we show using the Stuart-Landau model that such multiple transitions do not only occur in excitable systems, but also in oscillatory ones. 相似文献
13.
A famous phenomenon in circle-maps and synchronisation problems leads to a two-parameter bifurcation diagram commonly referred to as the Arnol′d tongue scenario. One considers a perturbation of a rigid rotation of a circle, or a system of coupled oscillators. In both cases we have two natural parameters, the coupling strength and a detuning parameter that controls the rotation number/frequency ratio. The typical parameter plane of such systems has Arnol′d tongues with their tips on the decoupling line, opening up into the region where coupling is enabled, and in between these Arnol′d tongues, quasi-periodic arcs. In this paper, we present unified algorithms for computing both Arnol′d tongues and quasi-periodic arcs for both maps and ODEs. The algorithms generalise and improve on the standard methods for computing these objects. We illustrate our methods by numerically investigating the Arnol′d tongue scenario for representative examples, including the well-known Arnol′d circle map family, a periodically forced oscillator caricature, and a system of coupled Van der Pol oscillators. 相似文献
14.
In this paper, we provide a novel reformulation of sufficient conditions that guarantee global complete synchronisation of coupled identical oscillators to make them computationally implementable. To this end, we use semidefinite programming techniques. For the first time, we can efficiently search for and obtain certificates for synchronisability and, additionally, also optimise associated cost functions. In this paper, a Lyapunov-like function (certificate) is used to certify that all trajectories of a networked system consisting of coupled dynamical systems will eventually converge towards a common one, which implies synchronisation. Moreover, we establish new conditions for complete synchronisation, which are based on the so called Bendixson’s Criterion for higher dimensional systems. This leads to major improvements on the lower bound of the coupling constant that guarantees global complete synchronisation. Importantly, the certificates are obtained by analysing the connection network and the model representing an individual system only. In order to illustrate the strength of our method we apply it to a system of coupled identical Lorenz oscillators and to coupled van der Pol oscillators. 相似文献
15.
Projective synchronisation with non-delayed and delayed coupling in complex networks consisting of identical nodes and different nodes 下载免费PDF全文
This paper first investigates the projective synchronisation problem with non-delayed and delayed coupling between drive-response dynamical networks consisting of identical nodes and different nodes.Based on Lyapunov stability theory,several nonlinear controllers are applied to achieve the projective synchronisation between the drive-response dynamical networks;simultaneously the topological structure of the drive dynamical complex networks can be exactly identified.Moreover,numerical examples are presented to verify the feasibility and effectiveness of the theorems. 相似文献
16.
This paper investigates the cluster-modified function projective synchronisation (CMFPS) of a generalised linearly coupled network with asymmetric coupling and nonidentical dynamical nodes. A novel synchronisation scheme is proposed to achieve CMFPS in community networks. We use adaptive control method to derive CMFPS criteria based on Lyapunov stability theory. Each cluster of networks is synchronised with target system by state transformation with scaling function matrix. Numerical simulation results are presented finally to illustrate the effectiveness of this method. 相似文献