Dong-Uk Hwang

Synchronization in complex networks with age ordering

The propensity for synchronization is studied in a complex network of asymmetrically coupled units, where the asymmetry in a given link is determined by the relative age of the involved nodes. In growing scale-free networks synchronization is enhanced when couplings from older to younger nodes are dominant. We describe the requirements for such an effect in a more general context and compare with the situations in non growing random networks with and without a degree ordering.

Synchronizing weighted complex networks

Real networks often consist of local units, which interact with each other via asymmetric and heterogeneous connections. In this work, we explore the constructive role played by such a directed and weighted wiring for the synchronization of networks of coupled dynamical systems. The stability condition for the synchronous state is obtained from the spectrum of the respective coupling matrices. In particular, we consider a coupling scheme in which the relative importance of a link depends on the number of shortest paths through it. We illustrate our findings for networks with different topologies: scale free, small world, and random wirings.

Exceptional points in coupled dissipative dynamical systems.

We study the transient behavior in coupled dissipative dynamical systems based on the linear analysis around the steady state. We find that the transient time is minimized at a specific set of system parameters and show that at this parameter set, two eigenvalues and two eigenvectors of the Jacobian matrix coalesce at the same time; this degenerate point is called the exceptional point. For the case of coupled limit-cycle oscillators, we investigate the transient behavior into the amplitude death state, and clarify that the exceptional point is associated with a critical point of frequency locking, as well as the transition of the envelope oscillation.

Estimation of inter-modular connectivity from the local field potentials in a hierarchical modular network

We propose a method of estimating inter-modular connectivity in a hierarchical modular network. The method is based on an analysis of inverse phase synchronization applied to the local field potentials on a hierarchical modular network of phase oscillators. For a strong-coupling strength, the inverse phase synchronization index of the local field potentials for two modules depends linearly on the corresponding inter-modular connectivity defined as the number of links connecting the modules. The method might enable us to estimate the inter-modular connectivity in various complex systems from the inverse phase synchronization index of the mesoscopic modular activities.

Stabilization of quasiperiodic output in a Q-switched Nd:YAG laser

Q-switched Nd:YAG laser produces various nonlinear dynamical behaviors such as period doubling, quasi-periodicity, intermittency, and chaos according to the modulation frequency and pumping rate. Our Q-switched Nd:YAG laser shows quasiperiodic output near 5 kHz of modulation frequency. Since this quasiperiodic outputs are undesirable in the application to drilling and marking, they should be stabilized for desired periods, period 1T, 2T, etc. In this report we introduce the method of stabilizing them for the desired period by using the return map of laser output. Explaining the core of it and we present the experimental results in detail.

Origin of the transition inside the desynchronized state in coupled chaotic oscillators

Abstract We investigate the origin of the transition inside the desynchronization state via phase jumps in coupled chaotic oscillators. We claim that the transition is governed by type-I intermittency in the presence of noise whose characteristic relation is 〈 l 〉∝exp( α | ϵ t − ϵ | 3/2 ) for ϵ t − ϵ l 〉∝( ϵ t − ϵ ) −1/2 for ϵ t − ϵ >0, where 〈 l 〉 is the average length of the phase locking state and ϵ is the coupling strength. To justify our claim we obtain analytically the tangent point, the bifurcation point, and the return map which agree well with those of the numerical simulations.

Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling

We study the collective behaviors in a ring of coupled nonidentical nonlinear oscillators with unidirectional coupling, of which natural frequencies are distributed in a random way. We find the amplitude death phenomena in the case of unidirectional couplings and discuss the differences between the cases of bidirectional and unidirectional couplings. There are three main differences; there exists neither partial amplitude death nor local clustering behavior but an oblique line structure which represents directional signal flow on the spatio-temporal patterns in the unidirectional coupling case. The unidirectional coupling has the advantage of easily obtaining global amplitude death in a ring of coupled oscillators with randomly distributed natural frequency. Finally, we explain the results using the eigenvalue analysis of the Jacobian matrix at the origin and also discuss the transition of dynamical behavior coming from connection structure as the coupling strength increases.

Is it right to estimate inter-modular connectivity from local field potentials?

Human brains with hundreds of billions of neurons are organized in a hierarchical modular network. There have been many attempts to estimate inter-modular connectivity utilizing coherent neuronal activities of a huge number of neurons, such as the electro-encephalogram, the magneto-encephalogram, and the functional magnetic resonance imaging. Here we ask a question: Is the inter-modular connectivity estimated from the modular activities consistent with the inter-modular connectivity that could be extracted from the network connectivity of individual nodes? To answer this question, we introduce a method of estimating the inter-modular connectivity based on the analysis of inverse phase synchronization [1,2]. For coupled phase oscillators on a hierarchical modular network shown in the Figure 1(A), the local field potential corresponding to a module is defined as the mean phase of oscillators belonging to a subset of the module. Figure 1 (A) A hierarchical modular network model 256-p-q-r, where p denotes the number of links of one node with nodes of its lower-level module, q links with nodes of the rest modules in its upper-level module, and r links with nodes of any modules from the ... For strong coupling strength, it is shown in Figure 1(B) that the inverse phase synchronization index grows linearly with the number of links connecting two modules. This result enables us to estimate the inter-modular connectivity in various complex systems from the inverse phase synchronization index of the mesoscopic modular activities.

Mechanism of synchronization in a random dynamical system.

The mechanism of synchronization in the random Zaslavsky map is investigated. From the error dynamics of two particles, the structure of phase space was analyzed, and a transcritical bifurcation between a saddle and a stable fixed point was found. We have verified the structure of on-off intermittency in terms of a biased random walk. Furthermore, for the generalized case of the ensemble of particles, a modified definition of the size of a snapshot attractor was exploited to establish the link with a random walk. As a result, the structure of on-off intermittency in the ensemble of particles was explicitly revealed near the transition.