Research Interest
Topological Methods in Dynamical Systems and Networks, Equivariant Degree Theory and Applications,
System Singularity and Bifurcations, Coupled Cell Networks and Synchrony-Breaking Bifurcations, Symmetry and Symmetry Breaking.
Papers
- I. Ovsyannikov and H. Ruan, Classication of codimension-1 singular bifurcation in low-dimensional DAEs,
Front. Appl. Math. Stat., 18 March 2022 Sec. Dynamical Systems
Link
- M.A.D. Aguiar, A.P.S. Dias and H. Ruan, Synchrony patterns in gene regulatory networks,
Physica D., 429 (2022), 133065
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- H. Ruan, Hidden symmetries, coupled networks and equivariant degrees, Int. J. Bifurc. Chaos, Volume No. 31, Issue No. 05, Article No. 2150073, 2021
Link
- H. Kamei and H. Ruan, Reduced lattices of synchrony subspaces and their indices, accepted in SIADS, 2020
arXiv
- H. Ruan and J. Zanelli, Degeneracy index and Poincaré-Hopf Theorem, submitted, 2020
arXiv
- M. Aguiar, A. Dias and H. Ruan, Synchrony and elementary operations on coupled cell networks, SIAM J. Appl. Dyn. Syst., 15(1), 2016, 322–337
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- F. Atay and H. Ruan, Symmetry analysis of coupled scalar systems under time delay, Nonlinearity 28 (2015) 795-824
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- M. Aguiar and H. Ruan, Evolution of synchrony under combination of coupled cell networks, Nonlinearity 25 (2012) 3155-3187.
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- H. Ruan, A degree theory for coupled cell systems with quotient symmetries, Nonlinearity 25 (2012) 2681-2716.
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- M. Aguiar and H. Ruan, Interior symmetries and real multiple eigenvalues for homogeneous networks, SIAM J. Appl. Dyn. Syst. 11, 1231-1269 (2012).
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- H. Ruan, Fixed points in absolutely irreducible real representations,
the Illinois Journal of Mathematics, Volume 55, Number 4, Winter 2011, 1551–1567.
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- N. Hirano, W. Krawcewicz and H. Ruan, Existence of nonstationary periodic solutions for
Γ-symmetric Lotka-Volterra type systems, Discrete Contin. Dyn. Syst-A, 30, No. 3 (2011), 709 - 735.
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- J. Fura, A. Golebiewska and H. Ruan, Existence of nonstationary periodic solutions for
Γ-symmetric asymptotically linear autonomous Newtonian systems with degeneracy,
Rocky Moun. J. Mat., 40, No.3 (2010), 873-911.
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- Z. Balanov, W. Krawcewicz and H. Ruan, Periodic solutions to O(2)-symmetric variational problems:
O(2)×S1-equivariant orthogonal degree approach, Contemporary Mathematics, 514 (2010), 45-84.
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- H. Ruan and S. Rybicki, Applications of equivariant degree for gradient maps to symmetric Newtonian
systems, Nonlinear Anal. TMA, 68 No.6 (2008) 1479-1516.
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- Z. Balanov, W. Krawcewicz, and H. Ruan, G. E. Hutchinson's delay logistic system with symmetries
and spatial diffusion, Nonlinear Anal. RWA 9 (2008) 154-182.
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- Z. Balanov, W. Krawcewicz, and H. Ruan, Hopf bifurcation in a symmetric configuration of lossless
transmission lines, Nonlinear Anal. RWA 8 (2007) 1144-1170.
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- Z. Balanov, M. Farzamirad, W. Krawcewicz, and H. Ruan, Applied equivariant degree,
part II: symmetric Hopf bifurcation for functional differential equations,
Discrete Contin. Dyn. Syst. Ser. A 16 No. 4 (2006) 923-960.
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- Z. Balanov, W. Krawcewicz and H. Ruan, Applied equivariant degree,
part I: an axiomatic approach to primary degree, Discrete Contin. Dyn. Syst. Ser. A 15,
No. 3 (2006) 983-1016.
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- Z. Balanov, W. Krawcewicz, and H. Ruan, Applied equivariant degree, part III:
Global symmetric Hopf bifurcation for functional differential equations, Proc. Latv. Acad. Sci. Sec B Nat.
Exact Appl. Sci. 59 No.6 (641) (2005) 234-240.
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Theses
- Habiliation Thesis: An equivariant degree theory for networked dynamical systems. 2017
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- Doctoral Thesis: A recent development of the equivariant degree methods and their applications in symmetric dynamical systems. 2008
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