Hopf's bifurcation theorem and the center theorem of Liapunov with resonance cases
From MaRDI portal
Publication:1248749
DOI10.1016/0022-247X(78)90081-1zbMath0383.34026MaRDI QIDQ1248749
Publication date: 1978
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)
Related Items
The Impact of Damping in Second-Order Dynamical Systems with Applications to Power Grid Stability, Classification and unfoldings of \(1:2\) resonant Hopf bifurcation, An invariant manifold approach to nonlinear normal modes of oscillation, Degenerate Hopf bifurcation in two dimensions, An optimal control problem applied to plasmid-mediated antibiotic resistance, Periodic solutions near an equilibrium of a differential equation with a first integral, Assessing the role of bacterial plasmid replication in a competition model of sensitive and resistant bacteria to antibiotics, Classification and unfoldings of degenerate Hopf bifurcations, A note on Liapunov's center theorem, Long periodic solutions near an equilibrium in general resonance cases, Remarks on the existence and the non-existence of some kind of periodic orbits for Hamiltonian systems, Existence of small periodic solutions of ordinary differential equations in \(\mathbb{R}^2\), Degenerate resonances and branching of periodic orbits, Properties of Center Manifolds, Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem, Stability and periodic solutions for a model of bacterial resistance to antibiotics caused by mutations and plasmids, Symmetric Liapunov center theorem for minimal orbit, Resonant codimension two bifurcation in a neutral functional differential equation, Existence of small periodic solutions of ordinary differential equations in \(\mathbb{R}^2\), INSTABILITY IN THE PRESENCE OF AN INDEFINITE CONSERVATION LAW, Computation of Periodic Solutions of Conservative Systems with Application to the 3-Body Problem, Unnamed Item, Integral averaging and bifurcation, An abstract setting for the study of the Hopf bifurcation, Lyapunov orbits in the \(n\)-vortex problem, Bifurcation formulas for O.D.E.'S in n, Global Hopf bifurcation from a multiple eigenvalue, Long periodic orbits near an equilibrium and the averaging method in higher-order resonances, A MODEL ON BACTERIAL RESISTANCE CONSIDERING A GENERALIZED LAW OF MASS ACTION FOR PLASMID REPLICATION, On the existence of long periodic orbits near the Lyapunov's periodic family in general reasonance cases, Invariant manifolds for Volterra integral equations of convolution type, A classical approach to the analyticity problem of center manifolds
Cites Work
- A unifying theory in determining periodic families for Hamiltonian systems at resonance
- The bifurcation of one or more closed orbits from an equilibrium point of an autonomous differential system
- Lyapunov's center theorem for resonant equilibrium
- Averaging and Bifurcations in Symmetric Systems
- Global Bifurcations of Periodic Orbits
- Periodic orbits near ?4 for mass ratios near the critical mass ratio of routh
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
