Corpus ID: 73632106

Bifurcation of space periodic solutions in symmetric reversible FDEs

@article{Balanov2016BifurcationOS,
  title={Bifurcation of space periodic solutions in symmetric reversible FDEs},
  author={Zalman Balanov and Haotian Wu},
  journal={arXiv: Dynamical Systems},
  year={2016}
}
In this paper, we propose an equivariant degree based method to study bifurcation of periodic solutions (of constant period) in symmetric networks of reversible FDEs. Such a bifurcation occurs when eigenvalues of linearization move along the imaginary axis (without change of stability of the trivial solution and possibly without $1:k$ resonance). Physical examples motivating considered settings are related to stationary solutions to PDEs with non-local interaction: reversible mixed delay… Expand
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References

SHOWING 1-10 OF 25 REFERENCES
Reversible Equivariant Hopf Bifurcation
Abstract.In this paper we study codimension-one Hopf bifurcation from symmetric equilibrium points in reversible equivariant vector fields. Such bifurcations are characterized by a doubly degenerateExpand
Hopf Bifurcation in Symmetric Networks of Coupled Oscillators with Hysteresis
The standard approach to study symmetric Hopf bifurcation phenomenon is based on the usage of the equivariant singularity theory developed by M. Golubitsky et al. In this paper, we present theExpand
Hopf bifurcation for equivariant conservative and time-reversible systems
We study the bifurcation of small periodic solutions at a non-semi-simple 1:1-resonance in equivariant conservative or equivariant time-reversible systems. By using an equivariant Liapunov-SchmidtExpand
Multiple periodic solutions for Γ-symmetric Newtonian systems
Abstract The existence of periodic solutions in Γ-symmetric Newtonian systems x ¨ = − ∇ f ( x ) can be effectively studied by means of the Γ × O ( 2 ) -equivariant gradient degree with values in theExpand
Branches of Periodic Orbits in Reversible Systems
In the typical reversible systems which appear in many applications (symmetric) periodic solutions appear in one-parameter families. In this short survey we describe how these branches of periodicExpand
On a class of nonlinear Schrödinger equations
AbstractThis paper concerns the existence of standing wave solutions of nonlinear Schrödinger equations. Making a standing wave ansatz reduces the problem to that of studying the semilinear ellipticExpand
Time-reversal symmetry in dynamical systems: a survey
Abstract In this paper we survey the topic of time-reversal symmetry in dynamical systems. We begin with a brief discussion of the position of time-reversal symmetry in physics. After definingExpand
Reversible Equivariant Linear Systems
In this paper we classify the structure of linear reversible systems (vector fields) on Rn that are equivariant with respect to a linear representation of a compact Lie group H. We assume theExpand
Theory of Degrees with Applications to Bifurcations and Differential Equations
Elements of Differential Topology. Degree in Finite--Dimensional Spaces. Leray--Schauder Degree for Compact Fields. Nussbaum--Sadovskii Degree for Condensing Fields. Applications to BifurcationExpand
Normal forms and unfoldings of linear systems in eigenspaces of (anti)-automorphisms of order two
Abstract In this article we classify normal forms and unfoldings of linear maps in eigenspaces of (anti)-automorphisms of order two. Our main motivation is provided by applications to linear systemsExpand
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