Restrictions and unfolding of double Hopf bifurcation in functional differential equations
From MaRDI portal
Publication:1868908
DOI10.1016/S0022-0396(02)00179-1zbMath1032.34068OpenAlexW2054848609MaRDI QIDQ1868908
Pietro-Luciano Buono, Jacques Bélair
Publication date: 28 April 2003
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/s0022-0396(02)00179-1
Related Items (25)
Equivariant normal forms for parameterized delay differential equations with applications to bifurcation theory ⋮ Double Hopf bifurcation induces coexistence of periodic oscillations in a diffusive Ginzburg-Landau model ⋮ Computation of double Hopf points for delay differential equations ⋮ DYNAMICS AND DOUBLE HOPF BIFURCATIONS OF THE ROSE–HINDMARSH MODEL WITH TIME DELAY ⋮ Bifurcation and stability analysis of nonlinear waves in \(\mathbb {D}_n\) symmetric delay differential systems ⋮ Multiple scales for two-parameter bifurcations in a neutral equation ⋮ Multiple scales and normal forms in a ring of delay coupled oscillators with application to chaotic Hindmarsh-Rose neurons ⋮ Bifurcation in \(Z_{2}\)-symmetry quadratic polynomial systems with delay ⋮ Versal unfoldings for linear retarded functional differential equations. ⋮ DOUBLE HOPF BIFURCATION FOR STUART–LANDAU SYSTEM WITH NONLINEAR DELAY FEEDBACK AND DELAY-DEPENDENT PARAMETERS ⋮ BIFURCATION THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS: A SURVEY ⋮ Normal form for high-dimensional nonlinear system and its application to a viscoelastic moving belt ⋮ STABILITY AND HOPF BIFURCATION OF A MODIFIED DELAY PREDATOR-PREY MODEL WITH STAGE STRUCTURE ⋮ Two-parameter bifurcations in a network of two neurons with multiple delays ⋮ Double Hopf bifurcation for van der Pol-Duffing oscillator with parametric delay feedback control ⋮ Nonresonant Hopf-Hopf bifurcation and a chaotic attractor in neutral functional differential equations ⋮ Rotating and standing waves in a diffractive nonlinear optical system with delayed feedback under \(O(2)\) Hopf bifurcation ⋮ Center manifolds theorem for parameterized delay differential equations with applications to zero singularities ⋮ Hopf-transcritical bifurcation in retarded functional differential equations ⋮ Toroidal normal forms for bifurcations in retarded functional differential equations. I: Multiple Hopf and transcritical/multiple Hopf interaction ⋮ Nonlinear dynamics in tumor-immune system interaction models with delays ⋮ Robust heteroclinic cycles in delay differential equations ⋮ Double Hopf bifurcation in delayed reaction-diffusion systems ⋮ Normal form of double-Hopf singularity with 1:1 resonance for delayed differential equations ⋮ Hopf bifurcations in time-delay systems with band-limited feedback
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- A simple global characterization for normal forms of singular vector fields
- Singularities and groups in bifurcation theory. Volume II
- Introduction to functional differential equations
- Limit cycles, tori, and complex dynamics in a second-order differential equation with delayed negative feedback
- Bifurcation analysis of a class of first-order nonlinear delay-differential equations with reflectional symmetry
- Singularities of vector fields
- 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
- Restrictions on the possible flows of scalar retarded functional differential equations in neighborhoods of singularities
- Stability and Bifurcations of Equilibria in a Multiple-Delayed Differential Equation
- Realisation of ordinary differential equations by retarded functional differential equations in neighbourhoods of equilibrium points
This page was built for publication: Restrictions and unfolding of double Hopf bifurcation in functional differential equations