Degenerated singular cycles of inclination-flip type
Different types of scaling in the dynamics of period-doubling maps under external periodic driving.
Doubling bifurcation of a closed invariant curve in 3D maps
The object of the present paper is to give a qualitative description of the bifurcation mechanisms associated with a closed invariant curve in three-dimensional maps, leading to its doubling, not related to a standard doubling of tori. We propose an explanation on how a closed invariant attracting curve, born via Neimark-Sacker bifurcation, can be transformed into a repelling one giving birth to a new attracting closed invariant curve which has doubled...
Dynamic bifurcation diagrams for some models in economics and biology.
Dynamical analysis of an interleaved single inductor TITO switching regulator.
Estimate for the Number of Zeros of Abelian Integrals on Elliptic Curves
2000 Mathematics Subject Classification: Primary 34C07, secondary 34C08.We obtain an upper bound for the number of zeros of the Abelian integral.The work was partially supported by contract No 15/09.05.2002 with the Shoumen University “K. Preslavski”, Shoumen, Bulgaria.
Examples of bifurcation of periodic solutions to variational inequalities in
A bifurcation problem for variational inequalities is studied, where is a closed convex cone in , , is a matrix, is a small perturbation, a real parameter. The main goal of the paper is to simplify the assumptions of the abstract results concerning the existence of a bifurcation of periodic solutions developed in the previous paper and to give examples in more than three dimensional case.
Existence and distribution of limit cycles in a Hamiltonian system.
Generalized Hopf bifurcations and applications to planar quadratic systems
Generic saddle-node bifurcation for cascade second order ODEs on manifolds
Cascade second order ODEs on manifolds are defined. These objects are locally represented by coupled second order ODEs such that any solution of one of them can represent an external force for the other one. A generic saddle-node bifurcation theorem for 1-parameter families of cascade second order ODEs is proved.
Global attractor of a differentiable autonomous system on the plane
We study the structure of a differentiable autonomous system on the plane with non-positive divergence outside a bounded set. It is shown that under certain conditions such a system has a global attractor. The main result here can be seen as an improvement of the results of Olech and Meisters in [7,9] concerning the global asymptotic stability conjecture of Markus and Yamabe and the Jacobian Conjecture.
Global bifurcation from the Fučik spectrum
Global Existence of Periodic Solutions in a Delayed Tumor-Immune Model
This paper is devoted to the study of global existence of periodic solutions of a delayed tumor-immune competition model. Also some numerical simulations are given to illustrate the theoretical results
Higher order Poincaré-Pontryagin functions and iterated path integrals
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 in the IS-LM business cycle model with time delay.
Hopf bifurcation of integro-differential equations.
In-phase and antiphase complete chaotic synchronization in symmetrically coupled discrete maps.
Invariance of Poincaré-Lyapunov polynomials under the group of rotations.
Invariant curves from symmetry
We show that certain symmetries of maps imply the existence of their invariant curves.