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...

The computation of solution paths for continuation problems requires the solution of a sequence of nonlinear systems of equations. Each nonlinear system can be solved by computing the solution of a succession of linear systems of equations determined by Jacobian matrices associated with the nonlinear system of equations. Points on the solution path where the Jacobian matrix is singular are refe...

Feedback regulation of nonlinear dynamical systems inevitably leads to issues concerning static bifurcation. Static bifurcation in feedback systems is linked to degeneracies in the system zero dynamics. Accordingly, the obvious remedy is to change the system input-output structure, but there are other possibilities as well. In this paper we summarize the main results connecting bifurcation beha...

We investigate, both experimentally and theoretically, the period-doubling bifurcation to alternans in heart tissue. Previously, this phenomenon has been modeled with either smooth or border-collision dynamics. Using a modification of existing experimental techniques, we find a hybrid behavior: Very close to the bifurcation point, the dynamics is smooth, whereas further away it is border-collis...

Let us consider a multicomponent plasma containing electrons and positively charged ions of various kinds and described by the multiparticle distribution function f i = f i

We study three quasicontinuum approximations of a lattice model for crack propagation. The influence of the approximation on the bifurcation patterns is investigated. The estimate of the modeling error is applicable to near and beyond bifurcation points, which enables us to evaluate the approximation over a finite range of loading and multiple mechanical equilibria.

One of the most important tasks in nonlinear dynamics is the determination of bifurcation sets of various dynamical systems. If the dynamical equations are known, bifurcation points in parameter space can be detected by solving some specific fixed point equations. Using suitable continuation algorithms these bifurcation points can be traced in parameter space in order to compute bifurcation cur...

The direction of bifurcation of nontrivial solutions to the elliptic boundary value problem involving unilateral nonlocal boundary conditions is shown in a neighbourhood of bifurcation points of a certain type. Moreover, the stability and instability of bifurcating solutions as well as of the trivial solution is described in the sense of minima of the potential. In particular, an exchange of st...

This study provides some connections between bifurcations of onecomplex-parameter complex analytic families of maps of the complex plane C and bifurcations of more general two-real-parameter families of real analytic (or C or C∞) maps of the real plane R. We perform a numerical study of local bifurcations in the families of maps of the plane given by z 7→ F(C,α)(z, z) = z 2 + C + αz where z is ...

This paper discusses the insights that a bifurcation analysis can provide when designing mechanisms. A model, in the form of a set of coupled steady-state equations, can be derived to describe the mechanism. Solutions to this model can be traced through the mechanism's state versus parameter space via numerical continuation, under the simultaneous variation of one or more parameters. With this ...