BIFURCATION THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS: A SURVEY
DOI10.11948/2015057zbMath1452.34002OpenAlexW1880192673MaRDI QIDQ5121223
Publication date: 11 September 2020
Published in: Journal of Applied Analysis & Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.11948/2015057
Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Applications of operator theory to differential and integral equations (47N20) Bifurcation theory of functional-differential equations (34K18) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02)
Related Items (2)
Uses Software
Cites Work
- Spatio-temporal patterns of nonlinear oscillations in an excitatory ring network with delay
- Computation of non-smooth local centre manifolds
- Global continuation of nonlinear waves in a ring of neurons
- Attractivity and Hopf bifurcation
- Invariant manifolds
- Global continua of rapidly oscillating periodic solutions of state-dependent delay differential equations
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Equivariant normal forms for parameterized delay differential equations with applications to bifurcation theory
- Zero singularities in a ring network with two delays
- Finding periodic orbits in state-dependent delay differential equations as roots of algebraic equations
- Center manifolds theorem for parameterized delay differential equations with applications to zero singularities
- Normal forms, resonance and bifurcation analysis via the Carleman linearization
- Spatially nonhomogeneous equilibrium in a reaction-diffusion system with distributed delay
- Stability of nonlinear waves in a ring of neurons with delays
- Smooth bifurcation of symmetric periodic solutions of functional differential equations
- Global Hopf bifurcation for differential equations with state-dependent delay
- Hopf bifurcations in a reaction-diffusion population model with delay effect
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Hopf bifurcation calculations for functional differential equations
- Circulant matrices and differential-delay equations
- A simple global characterization for normal forms of singular vector fields
- Hopf bifurcation for functional and functional differential equations with infinite delay
- Dynamic behavior from bifurcation equations
- Applications of centre manifold theory
- Bifurcation from periodic solutions in functional difference equations
- Quasi-invariant manifolds, stability, and generalized Hopf bifurcation
- Singularities and groups in bifurcation theory. Volume II
- Ordinary differential equations which yield periodic solutions of differential delay equations
- On the nonlinear differential delay equation x'(t) = -f(x(t),x(t-1))
- An applicable Hopf bifurcation formula and instability of small periodic solutions of the Field-Noyes model
- The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
- Theory of functional differential equations. 2nd ed
- On the theory and application of the Hopf-Friedrich Bifurcation theory
- The range of periods of periodic solutions of \(x'(t)=-\alpha f(x(t-1))\)
- Global bifurcation of periodic solutions of some autonomous functional differential equations
- Integral averaging and bifurcation
- The Fuller index and global Hopf bifurcation
- Integrated semigroups and delay differential equations
- Introduction to functional differential equations
- On Bendixson's criterion
- Hopf bifurcating periodic orbits in a ring of neurons with delays
- Bifurcation of periodic solutions of delay differential equation with two delays.
- Versal unfoldings for linear retarded functional differential equations.
- Further reductions of normal forms for dynamical systems
- Stability and Hopf bifurcation in a diffusive logistic population model with nonlocal delay effect
- Hopf bifurcation analysis in a delayed Nicholson blowflies equation
- Equivariant versal unfoldings for linear retarded functional differential equations
- Remarks on the equivariant degree theory
- Theory and applications of partial functional differential equations
- Singularities of vector fields
- Restrictions and unfolding of double Hopf bifurcation in functional differential equations
- Bifurcations of periodic solutions of delay differential equations
- Reduced \(\text{SO}(3)\times S^1\)-equivariant degree with applications to symmetric bifurcation problems.
- Existence and bifurcation of periodic solutions of high-dimensional delay differential equations
- Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
- Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
- Stability and Hopf bifurcation for a population delay model with diffusion effects
- Bifurcation theory of functional differential equations
- Patterns in hierarchical networks of neuronal oscillators with \(\mathbb D_3\times \mathbb Z_3\) symmetry
- Stability and bifurcation in a reaction-diffusion model with nonlocal delay effect
- Two-parameter bifurcations in a network of two neurons with multiple delays
- The stable, center-stable, center, center-unstable, unstable manifolds
- Center manifold theory for functional differential equations of mixed type
- Pattern formation and continuation in a trineuron ring with delays
- Periodic and Steady-State Mode Interactions Lead to Tori
- Fixed point theory and nonlinear problems
- Degree Theory for Equivariant Maps. I
- Normal forms near critical points for differential equations and maps
- Equivariant Hopf bifurcation for neutral functional differential equations
- Delay Differential Equations
- Zero singularities of codimension two and three in delay differential equations
- Branching patterns of wave trains in the FPU lattice
- PATTERN FORMATION IN A RING NETWORK WITH DELAY
- Properties of Center Manifolds
- Normal forms for singularities of vector fields
- Generalized hopf bifurcation and h-asymptotic stability
- Some Historical Remarks Concerning Degree Theory
- Degree theory for equivariant maps, the general 𝑆¹-action
- Global Bifurcations of Periodic Orbits
- A Hopf Global Bifurcation Theorem for Retarded Functional Differential Equations
- Symmetric functional differential equations and neural networks with memory
- Theory and applications of Hopf bifurcations in symmetric functional differential equations
- An Equivariant Degree with Applications to Symmetric Bifurcation Problems. Part 1: Construction of the Degree
- A note on periodic solutions of the delay differential equation 𝑥’(𝑡)=-𝑓(𝑥(𝑡-1))
- Normal forms and Hopf bifurcation for partial differential equations with delays
- Generalized Hopf bifurcation in delay differential equations
This page was built for publication: BIFURCATION THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS: A SURVEY