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- Hyuckki Hong, Beom Jun Kim, M. Y. Choi, Hyunggyu Park
- Physical review. E, Statistical, nonlinear, and…
- 2004

While shorter characteristic path length has in general been believed to enhance synchronizability of a coupled oscillator system on a complex network, the suppressing tendency of the heterogeneity of the degree distribution, even for shorter characteristic path length, has also been reported. To see this, we investigate the effects of various factors such… (More)

- Hyunsuk Hong, Hyunggyu Park, Lei-Han Tang
- Physical review. E, Statistical, nonlinear, and…
- 2007

The onset of synchronization in a system of random frequency oscillators coupled through a random network is investigated. Using a mean-field approximation, we characterize sample-to-sample fluctuations for networks of finite size, and derive the corresponding scaling properties in the critical region. For scale-free networks with the degree distribution… (More)

- Hyunsuk Hong, Meesoon Ha, Hyunggyu Park
- Physical review letters
- 2007

A finite-size-scaling (FSS) theory is proposed for various models in complex networks. In particular, we focus on the FSS exponent, which plays a crucial role in analyzing numerical data for finite-size systems. Based on the droplet-excitation (hyperscaling) argument, we conjecture the values of the FSS exponents for the Ising model, the… (More)

- Hyunsuk Hong, Hugues Chaté, Hyunggyu Park, Lei-Han Tang
- Physical review letters
- 2007

The entrainment transition of coupled random frequency oscillators is revisited. The Kuramoto model (global coupling) is shown to exhibit unusual sample-dependent finite-size effects leading to a correlation size exponent nu=5/2. Simulations of locally coupled oscillators in d dimensions reveal two types of frequency entrainment: mean-field behavior at d>4… (More)

- Meesoon Ha, Hyunsuk Hong, Hyunggyu Park
- Physical review letters
- 2006

We present an analysis of the classical contact process on scale-free networks. A mean-field study, both for finite and infinite network sizes, yields an absorbing-state phase transition at a finite critical value of the control parameter, characterized by a set of exponents depending on the network structure. Since finite size effects are large and the… (More)

- Jaegon Um, Hyunsuk Hong, Hyunggyu Park
- Physical review. E, Statistical, nonlinear, and…
- 2014

We consider a system of phase oscillators with random intrinsic frequencies coupled through sparse random networks and investigate how the connectivity disorder affects the nature of collective synchronization transitions. Various distribution types of intrinsic frequencies are considered: uniform, unimodal, and bimodal distribution. We employ a… (More)

- Hyunsuk Hong, Jaegon Um, Hyunggyu Park
- Physical review. E, Statistical, nonlinear, and…
- 2013

We consider one typical system of oscillators coupled through disordered link configurations in networks, i.e., a finite population of coupled phase oscillators with distributed intrinsic frequencies on a random network. We investigate the collective synchronization behavior, paying particular attention to link-disorder fluctuation effects on the… (More)

- Hyuckki Hong, Hyunggyu Park, M. Y. Choi
- Physical review. E, Statistical, nonlinear, and…
- 2005

We study collective behavior of locally coupled limit-cycle oscillators with random intrinsic frequencies, spatially extended over d -dimensional hypercubic lattices. Phase synchronization as well as frequency entrainment are explored analytically in the linear (strong-coupling) regime and numerically in the nonlinear (weak-coupling) regime. Our analysis… (More)

- Hyun Keun Lee, Beom Jun Kim, Hyunggyu Park
- Physical review. E, Statistical, nonlinear, and…
- 2011

The explosive percolation problem on the complete graph is investigated via extensive numerical simulations. We obtain the cluster-size distribution at the moment when the cluster size heterogeneity becomes maximum. The distribution is found to be well described by the power-law form with the decay exponent τ=2.06(2), followed by a hump. We then use the… (More)

- Hyunsuk Hong, Hugues Chaté, Lei-Han Tang, Hyunggyu Park
- Physical review. E, Statistical, nonlinear, and…
- 2015

We revisit the Kuramoto model to explore the finite-size scaling (FSS) of the order parameter and its dynamic fluctuations near the onset of the synchronization transition, paying particular attention to effects induced by the randomness of the intrinsic frequencies of oscillators. For a population of size N, we study two ways of sampling the intrinsic… (More)