Research Interest
Topological methods in nonlinear analysis, equivariant degree theory,
equivariant bifurcation theory, pattern formation in dynamical systems,
equivariant variational problems, coupled networks and synchronizations.
Papers
- 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 (2012).
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- H. Ruan, Fixed points in absolutely irreducible real representations,
the Illinois Journal of Mathematics, to appear.
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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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