Bifurcation of solutions of separable parameterized equations into lines.
Bifurcation results for a class of perturbed Fredholm maps.
Bifurcations in the two imaginary centers problem
In this paper we show that, for a given value of the energy, there is a bifurcation for the two imaginary centers problem. For this value not only the configuration of the orbits changes but also a change in the topology of the phase space occurs.
Breaking the continuity of a piecewise linear map
Knowledge about the behavior of discontinuous piecewise-linear maps is important for a wide range of applications. An efficient way to investigate the bifurcation structure in 2D parameter spaces of such maps is to detect specific codimension-2 bifurcation points, called organizing centers, and to describe the bifurcation structure in their neighborhood. In this work, we present the organizing centers in the 1D discontinuous piecewise-linear map...
Critical bifurcation surfaces of 3D discrete dynamics.
Double Hopf bifurcation with strong resonances in delayed systems with nonlinearities.
Global bifurcation result for the -biharmonic operator.
Le système de Hénon-Heiles
Numerical bifurcation of separable parameterized equations.
On the critical periods of Liénard systems with cubic restoring forces.
On the existence and stability of unfoldings of equivariant two-parameter bifurcation problems.
One-Parameter Bifurcation Analysis of Dynamical Systems using Maple
This paper presents two algorithms for one-parameter local bifurcations of equilibrium points of dynamical systems. The algorithms are implemented in the computer algebra system Maple 13 © and designed as a package. Some examples are reported to demonstrate the package’s facilities.* This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02–359/2008.
Organizing centers in parameter space of discontinuous 1D maps. The case of increasing/decreasing branches
This work contributes to classify the dynamic behaviors of piecewise smooth systems in which border collision bifurcations characterize the qualitative changes in the dynamics. A central point of our investigation is the intersection of two border collision bifurcation curves in a parameter plane. This problem is also associated with the continuity breaking in a fixed point of a piecewise smooth map. We will relax the hypothesis needed in [4] where...
Path formulation for a modal family.
Uniqueness of rapidly oscillating periodic solutions to a singularly perturbed differential-delay equation.