In this paper, we study the solution eld M of a class of nonlinear parametrized two-point boundary value problems. Typical representatives of this class are the shell equations of Bauer, Reiss, Keller 1] and Troger, Steindl 24]. The boundary value problems are formulated as an abstract operator equation T (x;) = 0 in appropriate Banach spaces of diierentiable functions. By exploiting the equiva...

Using an equation-free analysis approach we identify a Hopf bifurcation point and perform a twoparameter continuation of the Hopf point for the macroscopic dynamical behavior of an interacting particle model. Due to the nature of systems with a moderate number of particles and noise, the quality of the available numerical information requires the use of very robust numerical algorithms for each...

Numerically studies have shown that the bi-stability and backward bifurcation are not automatically connected in epidemic models. In fact, when a backward bifurcation occurs, the disease-free equilibrium may be globally stable or it may support to a stable limit cycle. In this paper, a continuous epidemic model that incorporates density-dependent treatments is analyzed. It is shown that it supp...

After a short review of various ways to calculate the Maslov index appearing in semiclassical Gutzwiller type trace formulae, we discuss a coordinate-independent and canonically invariant formulation recently proposed by A Sugita (2000, 2001). We give explicit formulae for its ingredients and test them numerically for periodic orbits in several Hamiltonian systems with mixed dynamics. We demons...

Properties of small amplitude oscillations of the single reed woodwind instruments near the oscillation threshold are investigated. Analytical formulae with explicit dependence on the physical parameters of the instrument and instrumentist allow to determine the bifurcation point, the nature of the bifurcation, the amplitude of the first harmonics and the oscillation frequency. The model, which...

A delayed predator-preymodel with disease in the prey is investigated. The conditions for the local stability and the existence of Hopf bifurcation at the positive equilibrium of the system are derived. The effect of the two different time delays on the dynamical behavior has been given. Numerical simulations are performed to illustrate the theoretical analysis. Finally, the main conclusions ar...

Minimal surfaces bounded by a polygon ? IR q (q 2) correspond in a one-to-one mannner to the critical points of Shiiman's function. For arbitrary, but xed polygons this function was investigated numerically in 16]. The present work extends the results in 16] to classes of polygons ? = ?(), where varies in certain subsets of nite dimensional spaces the dimensions of depending on the number of ve...

An autonomous free-running Ćuk converter is studied in this paper. Analysis of the describing nonlinear state equations shows that the system loses stability via a supercritical Hopf bifurcation. The boundary of stability is derived and local trajectories of motion studied. Cycle-by-cycle simulations of the actual system reveal the typical bifurcation from a stable equilibrium state to chaos, v...

This paper discusses a problem of the Hopf bifurcation control for a mathematical model of intracellular calcium oscillations by calculating the curvature coefficient of limit cycle and the bifurcation control theory. We find that the appearance and disappearance of calcium oscillations in this system are due to the supercritical and subcritical Hopf bifurcation of equilibrium points, respectiv...

In this paper, the bifurcation criteria for inductive power transfer (IPT) systems is suggested considering the inductive power pad losses. The bifurcation criteria for series-series (SS) and series-parallel (SP) topologies are derived in terms of the main parameters of the IPT system. For deriving precise criteria, power pad resistance is obtained by copper loss calculation and core loss analy...