we consider the bifurcation of periodic solutions from an equilibrium point of the given equation: x =f(x,?) , where x ? r , ? is a vector of real parameters ? , ? , ... , ? and f:r x r ->r has at least second continuous derivations in variables

in this paper, the deformation of a thick-walled circular cylindrical shell of incompressible isotropic elastic material is considered. the shell, which is made of three-term strain energy function is subjected to the combined external and axial loading pressure. in order to obtain the relevant eigenvalues, which is the main objective of the work, the incremental equilibrium equations are so...

We describe the qualitative dynamics and bifurcation set for a laser with injected signal for small cavity detunings. The main organizing center is the Hopf-saddle-node bifurcation from where a secondary Hopf bifurcation of a periodic orbit originates. We show that the laser’s stable cw solution existing for low injections, also suffers a secondary Hopf bifurcation. The resonance structure of b...

One of the major routes to chaotic scattering is through an abrupt bifurcation by which a nonattracting chaotic saddle is created as a system parameter changes through a critical value. In a previously investigated case, however, the fractal dimension of the set of singularities in the scattering function changes continuously through the bifurcation. We describe a type of abrupt bifurcation to ...

The quenching of alternans is considered using a nonlinear cardiac conduction model. The model consists of a nonlinear discrete-time piecewise smooth system. Several authors have hypothesized that alternans arise in the model through a period doubling bifurcation. In this work, it is first shown that the alternans exhibited by the model actually arise through a period doubling border collision ...

In this paper we study the qualitative behavior of a predator–prey system with nonmonotonic functional response. The system undergoes a series of bifurcations including the saddle-node bifurcation, the supercritical Hopf bifurcation, and the homoclinic bifurcation. For different parameter values the system could have a limit cycle or a homoclinic loop, or exhibit the socalled “paradox of enrich...