Nonautonomous bifurcation patterns for one-dimensional differential equations

DOI10.1016/j.jde.2006.11.002zbMath1125.34032OpenAlexW1984922486MaRDI QIDQ870103

Martin Rasmussen

Publication date: 12 March 2007

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2006.11.002

zbMATH Keywords

attractorrepellernon-autonomous differential equationattractive solutionNon-autonomous bifurcation theoryrepulsive solution

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Asymptotic properties of solutions to ordinary differential equations (34D05) Local and nonlocal bifurcation theory for dynamical systems (37G99) Nonautonomous smooth dynamical systems (37C60)

Related Items

NONAUTONOMOUS SADDLE-NODE BIFURCATIONS IN THE QUASIPERIODICALLY FORCED LOGISTIC MAP, Dynamics of a single species in a fluctuating environment under periodic yield harvesting, Finite-time attractivity and bifurcation for nonautonomous differential equations, Nonautonomous gradient-like vector fields on the circle: classification, structural stability and autonomization, Persistence and imperfection of nonautonomous bifurcation patterns, Bifurcation theory of attractors and minimal sets in d-concave nonautonomous scalar ordinary differential equations, NONAUTONOMOUS BIFURCATION OF BOUNDED SOLUTIONS: CROSSING CURVE SITUATIONS, Nonautonomous Dynamical Systems in the Life Sciences, Li–Yorke chaos in nonautonomous Hopf bifurcation patterns—I, Nonautonomous bifurcation scenarios in SIR models, Bifurcations of asymptotically autonomous differential equations, Ruelle-Pollicott resonances of stochastic systems in reduced state space. Part II: Stochastic Hopf bifurcation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bifurcations in non-autonomous scalar equations
• Applications of centre manifold theory
• Manifolds, tensor analysis, and applications.
• Hopf bifurcation from non-periodic solutions of differential equations. II
• Attractors for random dynamical systems
• Non-smooth pitchfork bifurcations
• Pitchfork and transcritical bifurcations in systems with homogeneous nonlinearities and an almost periodic time coefficient
• A nonautonomous transcritical bifurcation problem with an application to quasi-periodic bubbles.
• Stability, instability, and bifurcation phenomena in non-autonomous differential equations
• Random attractors for the 3d stochastic navier-stokes equation with multiplicative white noise
• TWO-STEP TRANSITION IN NONAUTONOMOUS BIFURCATIONS: AN EXPLANATION
• A NONAUTONOMOUS SADDLE-NODE BIFURCATION PATTERN
• BIFURCATIONS AND CONTINUOUS TRANSITIONS OF ATTRACTORS IN AUTONOMOUS AND NONAUTONOMOUS SYSTEMS
• Pullback attractors in dissipative nonautonomous differential equations under discretization