A citation-based method for searching scientific literature

Numerical phase reduction beyond the first order approximation.
Michael Rosenblum, Arkady Pikovsky. Chaos 2019
Times Cited: 10






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List of co-cited articles
37 articles co-cited >1



Times Cited
  Times     Co-cited
Similarity


Phase reduction and phase-based optimal control for biological systems: a tutorial.
Bharat Monga, Dan Wilson, Tim Matchen, Jeff Moehlis. Biol Cybern 2019
30
6
60

Greater accuracy and broadened applicability of phase reduction using isostable coordinates.
Dan Wilson, Bard Ermentrout. J Math Biol 2018
26
6
60

Isochrons and phaseless sets.
J Guckenheimer. J Math Biol 1975
92
5
50

Phase reduction method for strongly perturbed limit cycle oscillators.
Wataru Kurebayashi, Sho Shirasaka, Hiroya Nakao. Phys Rev Lett 2013
20
4
40

Phase-amplitude reduction of transient dynamics far from attractors for limit-cycling systems.
Sho Shirasaka, Wataru Kurebayashi, Hiroya Nakao. Chaos 2017
22
4
40

Isostable reduction of periodic orbits.
Dan Wilson, Jeff Moehlis. Phys Rev E 2016
21
4
40

Weakly coupled oscillators in a slowly varying world.
Youngmin Park, Bard Ermentrout. J Comput Neurosci 2016
10
3
30

High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model.
Jonathan E Rubin, David Terman. J Comput Neurosci 2004
280
3
30

Phase reduction of a limit cycle oscillator perturbed by a strong amplitude-modulated high-frequency force.
Kestutis Pyragas, Viktor Novičenko. Phys Rev E Stat Nonlin Soft Matter Phys 2015
8
3
37

Phase-amplitude descriptions of neural oscillator models.
Kyle Ca Wedgwood, Kevin K Lin, Ruediger Thul, Stephen Coombes. J Math Neurosci 2013
23
3
30

On the phase reduction and response dynamics of neural oscillator populations.
Eric Brown, Jeff Moehlis, Philip Holmes. Neural Comput 2004
186
3
30

Global computation of phase-amplitude reduction for limit-cycle dynamics.
A Mauroy, I Mezić. Chaos 2018
12
3
30

Phase-amplitude response functions for transient-state stimuli.
Oriol Castejón, Antoni Guillamon, Gemma Huguet. J Math Neurosci 2013
19
3
30

Optimizing stability of mutual synchronization between a pair of limit-cycle oscillators with weak cross coupling.
Sho Shirasaka, Nobuhiro Watanabe, Yoji Kawamura, Hiroya Nakao. Phys Rev E 2017
8
2
25

Shear diversity prevents collective synchronization.
Ernest Montbrió, Diego Pazó. Phys Rev Lett 2011
26
2
20

Two types of quasiperiodic partial synchrony in oscillator ensembles.
Michael Rosenblum, Arkady Pikovsky. Phys Rev E Stat Nonlin Soft Matter Phys 2015
6
2
33

Dynamics of globally coupled oscillators: Progress and perspectives.
Arkady Pikovsky, Michael Rosenblum. Chaos 2015
74
2
20

Chimera states: the existence criteria revisited.
Gautam C Sethia, Abhijit Sen. Phys Rev Lett 2014
110
2
20

Generative models of cortical oscillations: neurobiological implications of the kuramoto model.
Michael Breakspear, Stewart Heitmann, Andreas Daffertshofer. Front Hum Neurosci 2010
188
2
20

Theoretical mechanics: crowd synchrony on the Millennium Bridge.
Steven H Strogatz, Daniel M Abrams, Allan McRobie, Bruno Eckhardt, Edward Ott. Nature 2005
134
2
20

Isostable reduction of oscillators with piecewise smooth dynamics and complex Floquet multipliers.
Dan Wilson. Phys Rev E 2019
13
2
20

Dynamics of limit-cycle oscillators subject to general noise.
Denis S Goldobin, Jun-Nosuke Teramae, Hiroya Nakao, G Bard Ermentrout. Phys Rev Lett 2010
33
2
20

Chimera states for coupled oscillators.
Daniel M Abrams, Steven H Strogatz. Phys Rev Lett 2004
479
2
20

Synchronization in complex oscillator networks and smart grids.
Florian Dörfler, Michael Chertkov, Francesco Bullo. Proc Natl Acad Sci U S A 2013
138
2
20

Interplay of coupling and common noise at the transition to synchrony in oscillator populations.
Anastasiya V Pimenova, Denis S Goldobin, Michael Rosenblum, Arkady Pikovsky. Sci Rep 2016
19
2
20

Phase reduction beyond the first order: The case of the mean-field complex Ginzburg-Landau equation.
Iván León, Diego Pazó. Phys Rev E 2019
11
2
20

Functional phase response curves: a method for understanding synchronization of adapting neurons.
Jianxia Cui, Carmen C Canavier, Robert J Butera. J Neurophysiol 2009
36
2
20

Phasic Burst Stimulation: A Closed-Loop Approach to Tuning Deep Brain Stimulation Parameters for Parkinson's Disease.
Abbey B Holt, Dan Wilson, Max Shinn, Jeff Moehlis, Theoden I Netoff. PLoS Comput Biol 2016
43
2
20

Phase-amplitude reduction far beyond the weakly perturbed paradigm.
Dan Wilson. Phys Rev E 2020
9
2
22

Asymptotic phase for stochastic oscillators.
Peter J Thomas, Benjamin Lindner. Phys Rev Lett 2014
20
2
20

Recent advances in coupled oscillator theory.
Bard Ermentrout, Youngmin Park, Dan Wilson. Philos Trans A Math Phys Eng Sci 2019
8
2
25

Optimal phase control of biological oscillators using augmented phase reduction.
Bharat Monga, Jeff Moehlis. Biol Cybern 2019
7
2
28

Biological rhythms and the behavior of populations of coupled oscillators.
A T Winfree. J Theor Biol 1967
614
2
20

Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience.
Peter Ashwin, Stephen Coombes, Rachel Nicks. J Math Neurosci 2016
69
2
20

Phase description of stochastic oscillations.
Justus T C Schwabedal, Arkady Pikovsky. Phys Rev Lett 2013
23
2
20

Phase-dependent modulation as a novel approach for therapeutic brain stimulation.
Ramin Azodi-Avval, Alireza Gharabaghi. Front Comput Neurosci 2015
16
2
20

A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations.
Peter A Tass. Biol Cybern 2003
216
2
20

Instability of spatial patterns and its ambiguous impact on species diversity.
Tobias Reichenbach, Erwin Frey. Phys Rev Lett 2008
44
1
10

Emergence of unusual coexistence states in cyclic game systems.
Junpyo Park, Younghae Do, Bongsoo Jang, Ying-Cheng Lai. Sci Rep 2017
14
1
10

Biodiversity in the cyclic competition system of three species according to the emergence of mutant species.
Junpyo Park. Chaos 2018
5
1
20

Various synchronous states due to coupling strength inhomogeneity and coupling functions in systems of coupled identical oscillators.
Junhyeok Kim, Joon-Young Moon, Uncheol Lee, Seunghwan Kim, Tae-Wook Ko. Chaos 2019
4
1
25

Emergence of stable polymorphisms driven by evolutionary games between mutants.
Weini Huang, Bernhard Haubold, Christoph Hauert, Arne Traulsen. Nat Commun 2012
26
1
10

Phase transitions for rock-scissors-paper game on different networks.
Attila Szolnoki, György Szabó. Phys Rev E Stat Nonlin Soft Matter Phys 2004
36
1
10

Understanding individual human mobility patterns.
Marta C González, César A Hidalgo, Albert-László Barabási. Nature 2008
820
1
10

Phase synchronization of chaotic oscillators.
Rosenblum, Pikovsky, Kurths. Phys Rev Lett 1996
835
1
10

Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games.
Tobias Reichenbach, Mauro Mobilia, Erwin Frey. Nature 2007
271
1
10

Nonlinear dynamics of the rock-paper-scissors game with mutations.
Danielle F P Toupo, Steven H Strogatz. Phys Rev E Stat Nonlin Soft Matter Phys 2015
22
1
10

Cyclical interactions with alliance-specific heterogeneous invasion rates.
Matjaz Perc, Attila Szolnoki, György Szabó. Phys Rev E Stat Nonlin Soft Matter Phys 2007
36
1
10

Colicin diversity: a result of eco-evolutionary dynamics.
L Pagie, P Hogeweg. J Theor Biol 1999
43
1
10

Basins of attraction for species extinction and coexistence in spatial rock-paper-scissors games.
Hongjing Shi, Wen-Xu Wang, Rui Yang, Ying-Cheng Lai. Phys Rev E Stat Nonlin Soft Matter Phys 2010
31
1
10


Co-cited is the co-citation frequency, indicating how many articles cite the article together with the query article. Similarity is the co-citation as percentage of the times cited of the query article or the article in the search results, whichever is the lowest. These numbers are calculated for the last 100 citations when articles are cited more than 100 times.

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