Bifurcation diagrams and Fomenko’s surgery on Liouville tori of the Kolossoff potential
Bifurcation for second-order Hamiltonian systems with periodic boundary conditions.
Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas [Book]
Bifurcation from Periodic Solutions in Functional Differential Equations.
Bifurcation in a model of the population dynamics.
Bifurcation of an invariant torus of a system of differential equations in the degenerate case.
Bifurcation of closed orbits from a limit cycle in
Bifurcation of heteroclinic orbits for diffeomorphisms
The paper deals with the bifurcation phenomena of heteroclinic orbits for diffeomorphisms. The existence of a Melnikov-like function for the two-dimensional case is shown. Simple possibilities of the set of heteroclinic points are described for higherdimensional cases.
Bifurcation of multi-bump homoclinics in systems with normal and slow variables.
Bifurcation of periodic and chaotic solutions in discontinuous systems
Chaos generated by the existence of Smale horseshoe is the well-known phenomenon in the theory of dynamical systems. The Poincaré-Andronov-Melnikov periodic and subharmonic bifurcations are also classical results in this theory. The purpose of this note is to extend those results to ordinary differential equations with multivalued perturbations. We present several examples based on our recent achievements in this direction. Singularly perturbed problems are studied as well. Applications are given...
Bifurcation of periodic points and normal form theory in reversible diffeomorphisms
Bifurcation of periodic solutions from inversion of stability of periodic O.D.E.'S.
Bifurcation of periodic solutions in a rotationally symmetric oscillation system.
Bifurcation of periodic solutions in differential inclusions
Ordinary differential inclusions depending on small parameters are considered such that the unperturbed inclusions are ordinary differential equations possessing manifolds of periodic solutions. Sufficient conditions are determined for the persistence of some of these periodic solutions after multivalued perturbations. Applications are given to dry friction problems.
Bifurcation of periodic solutions to differential inequalities in
Bifurcation of periodic solutions to nonlinear measure differential equations
The paper is devoted to the periodic bifurcation problems for generalizations of ordinary differential systems. The bifurcation is understood in the static sense of Krasnoselski and Zabreko. First, the conditions necessary for the given point to be bifurcation point for non autonomous generalized ordinary differential equations (based on the Kurzweil gauge type generalized integral) are proved. Then, as the main contribution, analogous results are obtained also for the nonlinear non autonomous measure...
Bifurcation of periodic solutions to variational inequalities in based on Alexander-Yorke theorem
Variational inequalities are studied, where is a closed convex cone in , , is a matrix, is a small perturbation, a real parameter. The assumptions guaranteeing a Hopf bifurcation at some for the corresponding equation are considered and it is proved that then, in some situations, also a bifurcation of periodic solutions to our inequality occurs at some . Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting at constructed...
Bifurcation of solutions of nonlinear Sturm-Liouville problems.
Bifurcation of solutions of separable parameterized equations into lines.
Bifurcation sequences in the dissipative systems with saddle equilibria