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. pdf

• H. Ruan, A degree theory for coupled cell systems with quotient symmetries, Nonlinearity 25 (2012) 2681-2716. pdf

• M. Aguiar and H. Ruan, Interior symmetries and real multiple eigenvalues for homogeneous networks, SIAM J. Appl. Dyn. Syst. 11, 1231 (2012). pdf

• H. Ruan, Fixed points in absolutely irreducible real representations, the Illinois Journal of Mathematics, to appear. pdf

• 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. pdf

• 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. pdf

• 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. pdf

• 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. pdf

• 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. pdf

• Z. Balanov, W. Krawcewicz, and H. Ruan, Hopf bifurcation in a symmetric configuration of lossless transmission lines, Nonlinear Anal. RWA 8 (2007) 1144-1170. pdf

• 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. pdf

• 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. pdf

• 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. pdf