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1.
Coupled limit cycle oscillators with instantaneous mutual coupling offer a useful but idealized mathematical paradigm for
the study of collective behavior in a wide variety of biological, physical and chemical systems. In most real-life systems
however the interaction is not instantaneous but is delayed due to finite propagation times of signals, reaction times of
chemicals, individual neuron firing periods in neural networks etc. We present a brief overview of the effect of time-delayed
coupling on the collective dynamics of such coupled systems. Simple model equations describing two oscillators with a discrete
time-delayed coupling as well as those describing linear arrays of a large number of oscillators with time-delayed global
or local couplings are studied. Analytic and numerical results pertaining to time delay induced changes in the onset and stability
of amplitude death and phase-locked states are discussed. A number of recent experimental and theoretical studies reveal interesting
new directions of research in this field and suggest exciting future areas of exploration and applications. 相似文献
2.
3.
We study dynamical behaviors in coupled nonlinear oscillators and find that under certain conditions, a whole coupled oscillator
system can cease oscillation and transfer to a globally nonuniform stationary state [i.e., the so-called oscillation death
(OD) state], and this phenomenon can be generally observed. This OD state depends on coupling strengths and is clearly different
from previously studied amplitude death (AD) state, which refers to the phenomenon where the whole system is trapped into
homogeneously steady state of a fixed point, which already exists but is unstable in the absence of coupling. For larger systems,
very rich pattern structures of global death states are observed. These Turing-like patterns may share some essential features
with the classical Turing pattern.
相似文献
4.
CHEN Hai-Ling YANG Jun-Zhong 《理论物理通讯》2009,51(3):460-464
In this work, we investigate the amplitude death in coupled system with small number of nonlinear oscillators. We show how the transitions to the partial and the complete amplitude deathes happen. We also show that the partial amplitude death can be found in globally coupled oscillators either. 相似文献
5.
A population of identical nonlinear oscillators, subject to random forces and coupled via a mean-field interaction, is studied in the thermodynamic limit. The model presents a nonequilibrium phase transition from a stationary to a time-periodic probability density. Below the transition line, the population of oscillators is in a quiescent state with order parameter equal to zero. Above the transition line, there is a state of collective rhythmicity characterized by a time-periodic behavior of the order parameter and all moments of the probability distribution. The information entropy of the ensemble is a constant both below and above the critical line. Analytical and numerical analyses of the model are provided. 相似文献
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The dynamics of coupled Lorenz circuits is investigated experimentally. The partial
amplitude death reported in {\em Phys. Rev.} E {\bf 72}, 057201 (2005) is verified
by physical experiments with electronic circuits. With the increase of coupling
constant, the coupled circuits undergo the transition from the breakdown of both the
reflection symmetry and the translational symmetry to the partial amplitude death.
Its stability is also confirmed by analysing the effects of noise. 相似文献
8.
We analyze a mean-field model of coupled oscillators with randomly distributed frequencies. This system is known to exhibit a transition to collective oscillations: for small coupling, the system is incoherent, with all the oscillators running at their natural frequencies, but when the coupling exceeds a certain threshold, the system spontaneously synchronizes. We obtain the first rigorous stability results for this model by linearizing the Fokker-Planck equation about the incoherent state. An unexpected result is that the system has pathological stability properties: the incoherent state is unstable above threshold, butneutrally stable below threshold. We also show that the system is singular in the sense that its stability properties are radically altered by infinitesimal noise. 相似文献
9.
Impulsively coupled systems are high-dimensional non-smooth systems that can exhibit rich and complex dynamics.This paper studies the complex dynamics of a non-smooth system which is unidirectionally impulsively coupled by three Duffing oscillators in a ring structure.By constructing a proper Poincare map of the non-smooth system,an analytical expression of the Jacobian matrix of Poincare map is given.Two-parameter Hopf bifurcation sets are obtained by combining the shooting method and the Runge-Kutta method.When the period is fixed and the coupling strength changes,the system undergoes stable,periodic,quasi-periodic,and hyper-chaotic solutions,etc.Floquet theory is used to study the stability of the periodic solutions of the system and their bifurcations. 相似文献
10.
This paper applies washout filter technology to amplitude
control of limit cycles emerging from Hopf bifurcation of the van der
Pol--Duffing system. The controlling parameters for the appearance
of Hopf bifurcation are given by the Routh--Hurwitz criteria.
Noticeably, numerical simulation indicates that the controllers
control the amplitude of limit cycles not only of the weakly nonlinear van
der Pol--Duffing system but also of the strongly nonlinear van der
Pol--Duffing system. In particular, the emergence of Hopf bifurcation
can be controlled by a suitable choice of controlling parameters.
Gain-amplitude curves of controlled systems are also drawn. 相似文献
11.
Cooperative behaviors of coupled nonidentical oscillators with the same equilibrium points 下载免费PDF全文
《中国物理 B》2021,30(10):100504-100504
The cooperative behaviors resulted from the interaction of coupled identical oscillators have been investigated intensively. However, the coupled oscillators in practice are nonidentical, and there exist mismatched parameters. It has been proved that under certain conditions, complete synchronization can take place in coupled nonidentical oscillators with the same equilibrium points, yet other cooperative behaviors are not addressed. In this paper, we further consider two coupled nonidentical oscillators with the same equilibrium points, where one oscillator is convergent while the other is chaotic,and explore their cooperative behaviors. We find that the coupling mode and the coupling strength can bring the coupled oscillators to different cooperation behaviors in unidirectional or undirected couplings. In the case of directed coupling,death islands appear in two-parameter spaces. The mechanism inducing these transitions is presented. 相似文献
12.
Collective stochastic resonance behaviors of two coupled harmonic oscillators driven by dichotomous fluctuating frequency 下载免费PDF全文
《中国物理 B》2021,30(6):60502-060502
The collective behaviors of two coupled harmonic oscillators with dichotomous fluctuating frequency are investigated,including stability, synchronization, and stochastic resonance(SR). First, the synchronization condition of the system is obtained. When this condition is satisfied, the mean-field behavior is consistent with any single particle behavior in the system. On this basis, the stability condition and the exact steady-state solution of the system are derived. Comparative analysis shows that, the stability condition is stronger than the synchronization condition, that is to say, when the stability condition is satisfied, the system is both synchronous and stable. Simulation analysis indicates that increasing the coupling strength will reduce the synchronization time. In weak coupling region, there is an optimal coupling strength that maximizes the output amplitude gain(OAG), thus the coupling-induced SR behavior occurs. In strong coupling region, the two particles are bounded as a whole, so that the coupling effect gradually disappears. 相似文献
13.
Synchronization in the system of coupled non-identical non-isochronous van der Pol-Duffing oscillators with inertial and dissipative coupling is discussed. Generalized Adler’s equation is obtained and investigated in the presence of all relevant factors affecting the synchronization (non-isochronism of the oscillators, their non-identity, coupling of the dissipative and inertial types). Characteristic symmetries are revealed for the Adler’s equation responsible for equivalence of some of the factors. Numerical study of the parameters space of the initial differential equations is carried out using the method of charts of dynamic regimes in the parameter planes. Results obtained by both these approaches are compared and discussed. 相似文献
14.
A mean-field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit. When the frequency distribution isbimodal, new results include subcritical spontaneous stationary synchronization of the oscillators, supercritical time-periodic synchronization, bistability, and hysteretic phenomena. Bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength, and theirnonlinear stability properties ascertained. 相似文献
15.
为了找到具有多个旋转中心的混沌系统的相同步与其动力学拓朴变化之间的对应关系,采用线性振幅线性耦合方法,研究了Lorenz系统和Duffing系统的相同步,首先对Lorenz系统和Duffing系统分别进行极坐标变换,在线性振幅耦合基础上计算了两个系统的平均旋转数和Lyapunov指数,发现,随耦合强度的增大,系统相同步与系统的Lyapunov指数跃变存在一一对应的关系,这表明具有多个旋转中心的混沌系统的相同步与系统动力学拓朴变化也存在着对应关系.
关键词:
Lyapunov指数
振幅耦合
相同步 相似文献
16.
Direct time delay feedback can make non-chaotic Chen
circuit chaotic. The chaotic Chen circuit with direct time delay
feedback possesses rich and complex dynamical behaviours. To reach a
deep and clear understanding of the dynamics of such circuits
described by delay differential equations, Hopf bifurcation in the
circuit is analysed using the Hopf bifurcation theory and the
central manifold theorem in this paper. Bifurcation points and
bifurcation directions are derived in detail, which prove to be
consistent with the previous bifurcation diagram. Numerical
simulations and experimental results are given to verify the
theoretical analysis. Hopf bifurcation analysis can explain and
predict the periodical orbit (oscillation) in Chen circuit with
direct time delay feedback. Bifurcation boundaries are derived using
the Hopf bifurcation analysis, which will be helpful for determining
the parameters in the stabilisation of the originally chaotic
circuit. 相似文献
17.
讨论了一类简化Lang-Kobayashi方程的Hopf 分岔的性质.根据分岔理论,给出了系统产生Hopf 分岔的临界时滞条件,然后利用中心流形定理和规范型理论得到了确定Hopf分岔方向和分岔周期解的稳定性计算公式.最后,用数值模拟对理论结果进行了验证.
关键词:
Lang-Kobayashi方程
时滞
Hopf分岔
稳定性 相似文献
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19.
Stability and Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback 下载免费PDF全文
The stability and the Hopf bifurcation of a nonlinear electromechanical coupling system with time delay feedback are studied.By considering the energy in the air-gap field of the AC motor,the dynamical equation of the electromechanical coupling transmission system is deduced and a time delay feedback is introduced to control the dynamic behaviors of the system.The characteristic roots and the stable regions of time delay are determined by the direct method,and the relationship between the feedback gain and the length summation of stable regions is analyzed.Choosing the time delay as a bifurcation parameter,we find that the Hopf bifurcation occurs when the time delay passes through a critical value.A formula for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is given by using the normal form method and the center manifold theorem.Numerical simulations are also performed,which confirm the analytical results. 相似文献
20.
Phase synchronization and synchronization frequency of two-coupled van der Pol oscillators with delayed coupling 下载免费PDF全文
In this paper, phase synchronization and the frequency of two synchronized van der Pol oscillators with delay coupling are studied. The dynamics of such a system are obtained using the describing function method, and the necessary conditions for phase synchronization are also achieved. Finding the vicinity of the synchronization frequency is the major advantage of the describing function method over other traditional methods. The equations obtained based on this method justify the phenomenon of the synchronization of coupled oscillators on a frequency either higher, between, or lower than the highest, in between, or lowest natural frequency of the aggregate oscillators. Several numerical examples simulate the different cases versus the various synchronization frequency delays. 相似文献