Research Interest

Dynamical systems, bifurcation theory, equivariant degree and equivariant bifurcations, topological classification and stability analysis of bifurcating branches of solutions, coupled cell networks and coupled cell systems, synchrony patterns and related bifurcations in coupled cell networks, applications of network dynamics in system biology.

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