@article{GongToenjesPikovsky2020,
  author    = {Gong, Chen Chris and T{\"o}njes, Ralf and Pikovsky, Arkady},
  title     = {Coupled M{\"o}bius maps as a tool to model Kuramoto phase synchronization},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {102},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {2},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.102.022206},
  pages     = {12},
  year      = {2020},
  abstract  = {We propose Mobius maps as a tool to model synchronization phenomena in coupled phase oscillators. Not only does the map provide fast computation of phase synchronization, it also reflects the underlying group structure of the sinusoidally coupled continuous phase dynamics. We study map versions of various known continuous-time collective dynamics, such as the synchronization transition in the Kuramoto-Sakaguchi model of nonidentical oscillators, chimeras in two coupled populations of identical phase oscillators, and Kuramoto-Battogtokh chimeras on a ring, and demonstrate similarities and differences between the iterated map models and their known continuous-time counterparts.},
  language  = {en}
}
@article{GongPikovskij2019,
  author    = {Gong, Chen Chris and Pikovskij, Arkadij},
  title     = {Low-dimensional dynamics for higher-order harmonic, globally coupled phase-oscillator ensembles},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {100},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {6},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.100.062210},
  pages     = {10},
  year      = {2019},
  abstract  = {The Kuramoto model, despite its popularity as a mean-field theory for many synchronization phenomenon of oscillatory systems, is limited to a first-order harmonic coupling of phases. For higher-order coupling, there only exists a low-dimensional theory in the thermodynamic limit. In this paper, we extend the formulation used by Watanabe and Strogatz to obtain a low-dimensional description of a system of arbitrary size of identical oscillators coupled all-to-all via their higher-order modes. To demonstrate an application of the formulation, we use a second harmonic globally coupled model, with a mean-field equal to the square of the Kuramoto mean-field. This model is known to exhibit asymmetrical clustering in previous numerical studies. We try to explain the phenomenon of asymmetrical clustering using the analytical theory developed here, as well as discuss certain phenomena not observed at the level of first-order harmonic coupling.},
  language  = {en}
}
@article{PeterGongPikovskij2019,
  author    = {Peter, Franziska and Gong, Chen Chris and Pikovskij, Arkadij},
  title     = {Microscopic correlations in the finite-size Kuramoto model of coupled oscillators},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {100},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {3},
  publisher = {American Physical Society},
  address   = {College Park},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.100.032210},
  pages     = {6},
  year      = {2019},
  abstract  = {Supercritical Kuramoto oscillators with distributed frequencies can be separated into two disjoint groups: an ordered one locked to the mean field, and a disordered one consisting of effectively decoupled oscillators-at least so in the thermodynamic limit. In finite ensembles, in contrast, such clear separation fails: The mean field fluctuates due to finite-size effects and thereby induces order in the disordered group. This publication demonstrates this effect, similar to noise-induced synchronization, in a purely deterministic system. We start by modeling the situation as a stationary mean field with additional white noise acting on a pair of unlocked Kuramoto oscillators. An analytical expression shows that the cross-correlation between the two increases with decreasing ratio of natural frequency difference and noise intensity. In a deterministic finite Kuramoto model, the strength of the mean-field fluctuations is inextricably linked to the typical natural frequency difference. Therefore, we let a fluctuating mean field, generated by a finite ensemble of active oscillators, act on pairs of passive oscillators with a microscopic natural frequency difference between which we then measure the cross-correlation, at both super- and subcritical coupling.},
  language  = {en}
}
@article{GongKlumpp2017,
  author    = {Gong, Chen Chris and Klumpp, Stefan},
  title     = {Modeling sRNA-Regulated Plasmid Maintenance},
  series = {PLoS one},
  volume    = {12},
  journal   = {PLoS one},
  publisher = {PLoS},
  address   = {San Fransisco},
  issn      = {1932-6203},
  doi       = {10.1371/journal.pone.0169703},
  pages     = {19},
  year      = {2017},
  abstract  = {We study a theoretical model for the toxin-antitoxin (hok/sok) mechanism for plasmid maintenance in bacteria. Toxin-antitoxin systems enforce the maintenance of a plasmid through post-segregational killing of cells that have lost the plasmid. Key to their function is the tight regulation of expression of a protein toxin by an sRNA antitoxin. Here, we focus on the nonlinear nature of the regulatory circuit dynamics of the toxin-antitoxin mechanism. The mechanism relies on a transient increase in protein concentration rather than on the steady state of the genetic circuit. Through a systematic analysis of the parameter dependence of this transient increase, we confirm some known design features of this system and identify new ones: for an efficient toxin-antitoxin mechanism, the synthesis rate of the toxin's mRNA template should be lower that of the sRNA antitoxin, the mRNA template should be more stable than the sRNA antitoxin, and the mRNA-sRNA complex should be more stable than the sRNA antitoxin. Moreover, a short half-life of the protein toxin is also beneficial to the function of the toxin-antitoxin system. In addition, we study a therapeutic scenario in which a competitor mRNA is introduced to sequester the sRNA antitoxin, causing the toxic protein to be expressed.},
  language  = {en}
}
@article{GongZhengToenjesetal.2019,
  author    = {Gong, Chen Chris and Zheng, Chunming and T{\"o}njes, Ralf and Pikovskij, Arkadij},
  title     = {Repulsively coupled Kuramoto-Sakaguchi phase oscillators ensemble subject to common noise},
  series = {Chaos : an interdisciplinary journal of nonlinear science},
  volume    = {29},
  journal   = {Chaos : an interdisciplinary journal of nonlinear science},
  number    = {3},
  publisher = {American Institute of Physics},
  address   = {Melville},
  issn      = {1054-1500},
  doi       = {10.1063/1.5084144},
  pages     = {11},
  year      = {2019},
  abstract  = {We consider the Kuramoto-Sakaguchi model of identical coupled phase oscillators with a common noisy forcing. While common noise always tends to synchronize the oscillators, a strong repulsive coupling prevents the fully synchronous state and leads to a nontrivial distribution of oscillator phases. In previous numerical simulations, the formation of stable multicluster states has been observed in this regime. However, we argue here that because identical phase oscillators in the Kuramoto-Sakaguchi model form a partially integrable system according to the Watanabe-Strogatz theory, the formation of clusters is impossible. Integrating with various time steps reveals that clustering is a numerical artifact, explained by the existence of higher order Fourier terms in the errors of the employed numerical integration schemes. By monitoring the induced change in certain integrals of motion, we quantify these errors. We support these observations by showing, on the basis of the analysis of the corresponding Fokker-Planck equation, that two-cluster states are non-attractive. On the other hand, in ensembles of general limit cycle oscillators, such as Van der Pol oscillators, due to an anharmonic phase response function as well as additional amplitude dynamics, multiclusters can occur naturally. Published under license by AIP Publishing.},
  language  = {en}
}
@phdthesis{Gong2019,
  author    = {Gong, Chen Chris},
  title     = {Synchronization of coupled phase oscillators},
  doi       = {10.25932/publishup-48752},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-487522},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xvii, 115},
  year      = {2019},
  abstract  = {Oscillatory systems under weak coupling can be described by the Kuramoto model of phase oscillators. Kuramoto phase oscillators have diverse applications ranging from phenomena such as communication between neurons and collective influences of political opinions, to engineered systems such as Josephson Junctions and synchronized electric power grids. This thesis includes the author's contribution to the theoretical framework of coupled Kuramoto oscillators and to the understanding of non-trivial N-body dynamical systems via their reduced mean-field dynamics. The main content of this thesis is composed of four parts. First, a partially integrable theory of globally coupled identical Kuramoto oscillators is extended to include pure higher-mode coupling. The extended theory is then applied to a non-trivial higher-mode coupled model, which has been found to exhibit asymmetric clustering. Using the developed theory, we could predict a number of features of the asymmetric clustering with only information of the initial state provided. The second part consists of an iterated discrete-map approach to simulate phase dynamics. The proposed map --- a Moebius map --- not only provides fast computation of phase synchronization, it also precisely reflects the underlying group structure of the dynamics. We then compare the iterated-map dynamics and various analogous continuous-time dynamics. We are able to replicate known phenomena such as the synchronization transition of the Kuramoto-Sakaguchi model of oscillators with distributed natural frequencies, and chimera states for identical oscillators under non-local coupling. The third part entails a particular model of repulsively coupled identical Kuramoto-Sakaguchi oscillators under common random forcing, which can be shown to be partially integrable. Via both numerical simulations and theoretical analysis, we determine that such a model cannot exhibit stationary multi-cluster states, contrary to the numerical findings in previous literature. Through further investigation, we find that the multi-clustering states reported previously occur due to the accumulation of discretization errors inherent in the integration algorithms, which introduce higher-mode couplings into the model. As a result, the partial integrability condition is violated. Lastly, we derive the microscopic cross-correlation of globally coupled non-identical Kuramoto oscillators under common fluctuating forcing. The effect of correlation arises naturally in finite populations, due to the non-trivial fluctuations of the meanfield. In an idealized model, we approximate the finite-sized fluctuation by a Gaussian white noise. The analytical approximation qualitatively matches the measurements in numerical experiments, however, due to other periodic components inherent in the fluctuations of the mean-field there still exist significant inconsistencies.},
  language  = {en}
}
@article{GongLibeskindTempeletal.2019,
  author    = {Gong, Chen Chris and Libeskind, Noam I. and Tempel, Elmo and Guo, Quan and Gottloeber, Stefan and Yepes, Gustavo and Wang, Peng and Sorce, Jenny and Pawlowski, Marcel},
  title     = {The origin of lopsided satellite galaxy distribution in galaxy pairs},
  series = {Monthly notices of the Royal Astronomical Society},
  volume    = {488},
  journal   = {Monthly notices of the Royal Astronomical Society},
  number    = {3},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0035-8711},
  doi       = {10.1093/mnras/stz1917},
  pages     = {3100 -- 3108},
  year      = {2019},
  abstract  = {It is well known that satellite galaxies are not isotropically distributed among their host galaxies as suggested by most interpretations of the Λ cold dark matter (ΛCDM) model. One type of anisotropy recently detected in the Sloan Digital Sky Survey (and seen when examining the distribution of satellites in the Local Group and in the Centaurus group) is a tendency to be so-called lopsided. Namely, in pairs of galaxies (like Andromeda and the Milky Way) the satellites are more likely to inhabit the region in between the pair, rather than on opposing sides. Although recent studies found a similar set-up when comparing pairs of galaxies in ΛCDM simulations indicating that such a set-up is not inconsistent with ΛCDM, the origin has yet to be explained. Here we examine the origin of such lopsided set-ups by first identifying such distributions in pairs of galaxies in numerical cosmological simulations, and then tracking back the orbital trajectories of satellites (which at z = 0 display the effect). We report two main results: first, the lopsided distribution was stronger in the past and weakens towards z = 0. Secondly, the weakening of the signal is due to the interaction of satellite galaxies with the pair. Finally, we show that the z = 0 signal is driven primarily by satellites that are on first approach, who have yet to experience a 'flyby'. This suggests that the signal seen in the observations is also dominated by dynamically young accretion events.},
  language  = {en}
}