Stability analysis for standing pulse solutions to FitzHugh-Nagumo equations
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Publication:2636861
DOI10.1007/s00526-013-0601-0zbMath1315.35030OpenAlexW2023620170MaRDI QIDQ2636861
Publication date: 18 February 2014
Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00526-013-0601-0
Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Second-order parabolic systems (35K40)
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Cites Work
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- Dissipative solitons in reaction diffusion systems. Mechanisms, dynamics, interaction
- Computing the Maslov index of solitary waves. I: Hamiltonian systems on a four-dimensional phase space
- Homoclinics for a Hamiltonian with wells at different levels
- An application of the modular function in nonlocal variational problem
- Some mathematical aspects of the micro-phase separation in diblock copolymers
- Pulse dynamics in a three-component system: Stability and bifurcations
- Stability of fast travelling pulse solutions of the FitzHugh-Nagumo equations
- The Sturm theorems and symplectic geometry
- Long time behavior of solutions of bistable nonlinear diffusion equations
- A geometric approach to singular perturbation problems with applications to nerve impulse equations
- The approach of solutions of nonlinear diffusion equations to travelling front solutions
- A positive solution on \(\mathbb{R}^N\) to a system of elliptic equations of FitzHugh-Nagumo type
- The Maslov index for paths
- Mini-maximizers for reaction-diffusion systems with skew-gradient structure
- Standing pulse solutions to FitzHugh-Nagumo equations
- Index theory for symplectic paths with applications
- Maslov-type index theory for symplectic paths and spectral flow. II
- Maslov-type index theory for symplectic paths and spectral flow. I
- Maslov index for homoclinic orbits of Hamiltonian systems
- Large stable pulse solutions in reaction-diffusion equations
- Singular Limit Analysis of Stability of Traveling Wave Solutions in Bistable Reaction-Diffusion Systems
- Stability Analysis for the Slow Travelling Pulse of the FitzHugh–Nagumo System
- Maslov indices in the Gutzwiller trace formula
- On the iteration of closed geodesics and the sturm intersection theory
- On the Maslov index of multi-pulse homoclinic orbits
- Dynamics of traveling pulses in heterogeneous media
- Stability of the Travelling Wave Solution of the Fitzhugh-Nagumo System
- Instability of standing waves for non-linear Schrödinger-type equations
- Spectral asymmetry and Riemannian geometry. III
- The Evans Function and Generalized Melnikov Integrals
- On the maslov index
- On the canonically invariant calculation of Maslov indices
- Winding number formula for Maslov indices
- The chemical basis of morphogenesis
- The Spectral Flow and the Maslov Index
- Stability of the in-phase travelling wave solutions in a pair of coupled nerve fibers
- Global Stability of Traveling Fronts and Convergence Towards Stacked Families of Waves in Monotone Parabolic Systems
- Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
- Three Sources and Three Component Parts of the Concept of Dissipative Solitons
- Interaction of dissipative solitons: Particle-like behaviour of localized structures in a three-component reaction-diffusion system
- Standing pulse solutions in reaction-diffusion systems with skew-gradient structure
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