A bifurcation result for Sturm-Liouville problems with a set-valued term.
A simple model of thermoelectric oscillations
A system of ordinary differential equations modelling an electric circuit with a thermistor is considered. Qualitative properties of solution are studied, in particular, the existence and nonexistence of time-periodic solutions (the Hopf bifurcation).
A survey on homoclinic and heterocolinic orbits.
A three-species food chain system with two types of functional responses.
A two parameters Ambrosetti-Prodi problem.
A viral infection model with a nonlinear infection rate.
Abelian integrals of quadratic Hamiltonian vector fields with an invariant straight line.
We prove that the lowest upper bound for the number of isolated zeros of the Abelian integrals associated to quadratic Hamiltonian vector fields having a center and an invariant straight line after quadratic perturbations is one.
Accurate reduction of a model of circadian rhythms by delayed quasi-steady state assumptions
Quasi-steady state assumptions are often used to simplify complex systems of ordinary differential equations in the modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original system and to have a small number of variables. This enables to use the stability and bifurcation analysis to reveal a deeper structure in the dynamics of the original system. This contribution shows that introducing delays to quasi-steady state assumptions...
An age-structured model of cannibalism.
Analytical stability analysis of periodic systems by Poincaré mappings with application to rotorcraft dynamics.
Application of the Lyapunov-Schmidt method to the problem of the branching of a cycle from a family of equilibria in a system with multicosymmetry.
Applications of global bifurcation to existence theorems for Sturm-Liouville problems
Asymmetric bound states of differential equations in nonlinear optics
Asymptotic Behavior of a Discrete Maturity Structured System of Hematopoietic Stem Cell Dynamics with Several Delays
We propose and analyze a mathematical model of hematopoietic stem cell dynamics. This model takes into account a finite number of stages in blood production, characterized by cell maturity levels, which enhance the difference, in the hematopoiesis process, between dividing cells that differentiate (by going to the next stage) and dividing cells that keep the same maturity level (by staying in the same stage). It is described by a system of n nonlinear differential equations with n delays. We study...
Asymptotic behaviour and Hopf bifurcation of a three-dimensional nonlinear autonomous system.
Basic algebro-geometric conceps in the study of planar polynomial vector fields.
In this work we show that basic algebro-geometric concepts such as the concept of intersection multiplicity of projective curves at a point in the complex projective plane, are needed in the study of planar polynomial vector fields and in particular in summing up the information supplied by bifurcation diagrams of global families of polynomial systems. Algebro-geometric concepts are helpful in organizing and unifying in more intrinsic ways this information.
Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation
The modified generalized Van der Pol-Mathieu equation is generalization of the equation that is investigated by authors Momeni et al. (2007), Veerman and Verhulst (2009) and Kadeřábek (2012). In this article the Bautin bifurcation of the autonomous system associated with the modified generalized Van der Pol-Mathieu equation has been proved. The existence of limit cycles is studied and the Lyapunov quantities of the autonomous system associated with the modified Van der Pol-Mathieu equation are computed....
Bifurcation diagram of a cubic three-parameter autonomous system.
Bifurcation diagrams and Fomenko’s surgery on Liouville tori of the Kolossoff potential