Center manifolds theorem for parameterized delay differential equations with applications to zero singularities

DOI10.1016/j.na.2011.04.003zbMath1365.34123OpenAlexW2049351827MaRDI QIDQ548619

Juanjuan Man, Shangjiang Guo

Publication date: 29 June 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2011.04.003

zbMATH Keywords

center manifoldBogdanov-Takens bifurcationfold bifurcation

Mathematics Subject Classification ID

Population dynamics (general) (92D25) Qualitative investigation and simulation of models involving functional-differential equations (34K60) Bifurcation theory of functional-differential equations (34K18) Invariant manifolds of functional-differential equations (34K19)

Related Items (9)

Bifurcations in the diffusive Bazykin model ⋮ Turing-Hopf bifurcation and spatiotemporal patterns in a diffusive predator-prey system with Crowley-Martin functional response ⋮ Codimension Bifurcation Analysis of a Modified Leslie–Gower Predator–Prey Model with Two Delays ⋮ Bifurcation Analysis of Bogdanov–Takens Bifurcations in Delay Differential Equations ⋮ Generalized Hopf Bifurcation for Neutral Functional Differential Equations ⋮ BIFURCATION THEORY OF FUNCTIONAL DIFFERENTIAL EQUATIONS: A SURVEY ⋮ Bifurcating periodic solution for a class of first-order nonlinear delay differential equation after Hopf bifurcation ⋮ Switching to Nonhyperbolic Cycles from Codimension Two Bifurcations of Equilibria of Delay Differential Equations ⋮ INTERACTIONS OF TURING AND HOPF BIFURCATIONS IN AN ADDITIONAL FOOD PROVIDED DIFFUSIVE PREDATOR-PREY MODEL

Uses Software

• Maple

Cites Work

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• Delay differential equations: with applications in population dynamics
• Center manifolds and normal forms for a class of retarded functional differential equations with parameter associated with Fold-Hopf singularity
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Applications of centre manifold theory
• Stability of some population models with delay
• Elements of applied bifurcation theory.
• Versal unfoldings for linear retarded functional differential equations.
• Predator-prey models with delay and prey harvesting
• Equivariant versal unfoldings for linear retarded functional differential equations
• Restrictions and unfolding of double Hopf bifurcation in functional 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
• The stable, center-stable, center, center-unstable, unstable manifolds
• Delay Differential Equations
• Zero singularities of codimension two and three in delay differential equations
• The Effects of Harvesting and Time Delay on Predator-prey Systems with Holling Type II Functional Response
• On Nonlinear Dynamics of Predator-Prey Models with Discrete Delay
• Properties of Center Manifolds
• Mixed block elimination for linear systems with wider borders
• Computation of non-smooth local centre manifolds
• Invariant manifolds

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