Homoclinic, Heteroclinic, and Periodic Orbits for a Class of Indefinite Hamiltonian Systems.
Hopf Bifurcation Analysis of Pathogen-Immune Interaction Dynamics With Delay Kernel
The aim of this paper is to study the steady states of the mathematical models with delay kernels which describe pathogen-immune dynamics of infectious diseases. In the study of mathematical models of infectious diseases it is important to predict whether the infection disappears or the pathogens persist. The delay kernel is described by the memory function that reflects the influence of the past density of pathogen in the blood and it is given by a nonnegative bounded and normated function k defined...
Hopf bifurcation for fully nonlinear equations in Banach space
Hopf bifurcation from a turning point.
Hopf bifurcation from infinity
Hopf bifurcation in symmetric systems
Hopf bifurcation with -symmetry.
Hopf bifurcations in a three-species food chain system with multiple delays
This paper is concerned with a three-species Lotka-Volterra food chain system with multiple delays. By linearizing the system at the positive equilibrium and analyzing the associated characteristic equation, the stability of the positive equilibrium and existence of Hopf bifurcations are investigated. Furthermore, the direction of bifurcations and the stability of bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem for functional differential equations....
Hoptf bifurcation from infinity for planar control systems.
Symmetric piecewise linear bi-dimensional systems are very common in control engineering. They constitute a class of non-differentiable vector fields for which classical Hopf bifurcation theorems are not applicable. For such systems, sufficient and necessary conditions for bifurcation of a limit cycle from the periodic orbit at infinity are given.
Hyperbolic characteristics on star-shaped hypersurfaces
Impulsive periodic boundary value problem
In the paper we consider the impulsive periodic boundary value problem with a general linear left hand side. The results are based on the topological degree theorems for the corresponding operator equation on a certain set that is established using properties of strict lower and upper functions of the boundary value problem.
Infinite cup length in free loop spaces with an application to a problem of the N-body type
Instability of solutions of certain nonlinear vector differential equations of third order.
Invariant tori for periodically perturbed oscillators.
The response of an oscillator to a small amplitude periodic excitation is discussed. In particular, sufficient conditions are formulated for the perturbed oscillator to have an invariant torus in the phase cylinder. When such an invariant torus exists, some perturbed solutions are in the basin of attraction of this torus and are thus entrained to the dynamical behavior of the perturbed system on the torus. In particular, the perturbed solutions in the basin of attraction of the invariant torus are...
Inverse problems connected with periods of oscillations described by ẍ + g(x) = 0
Isolated periodic minima are unstable
La théorie des perturbations au voisinage des systèmes hamiltoniens convexes
Large scale oscillatory behaviour in loaded asymmetric systems
L'existence d'une solution périodique d'une équation différentielle dans le cas où le second membre de l'équation n'est pas monotone par rapport à x
Limit cycles in a Kolmogorov-type model.