Cardiac arrhythmias have been closely linked to a variety of bifurcations and chaos. In this paper control of bifurcations and chaos for nonlinear models of cardiac electro-physiologic activity is investigated. Both the Andronov-Hopf bifurcation and period doubling bifur-cation are treated. Washout lter aided feedback controllers are employed to control the location and stability of the bifurca...

A codimension-three bifurcation, characterized by a pair of purely imaginary eigenvalues and a nonsemisimple double zero eigenvalue, arises in the study of a pair of weakly coupled nonlinear oscillators with Z2 Z2 symmetry. The methodology is based on Arnold's ideas of versal deformations of matrices for the linear analysis, and Poincar e normal forms for the nonlinear analysis of the system. B...

<p style='text-indent:20px;'>In this paper we study generalized Poincaré-Andronov-Hopf bifurcations of discrete dynamical systems. We prove a general result for attractors in <inline-formula><tex-math id="M1">\begin{document}$ n $\end{document}</tex-math></inline-formula>-dimensional manifolds satisfying some suitable conditions. This allows us to obtain sharper Ho...

A circuit model is proposed for studying the global behavior of the normal form describing the Bogdanov-Takens bifurcation, which is encountered in the study of autonomous dynamical systems arising in different branches of science and engineering. The circuit is easy-to-implement and one can experimentally study the rich dynamics and bifurcations simply by altering the values of some linear cir...

In this paper, we study the cubic three-parameter autonomous planar system ẋ1 = k1 + k2x1 − x1 − x2, ẋ2 = k3x1 − x2, where k2, k3 > 0. Our goal is to obtain a bifurcation diagram; i.e., to divide the parameter space into regions within which the system has topologically equivalent phase portraits and to describe how these portraits are transformed at the bifurcation boundaries. Results may be a...

We analyze a frequency decrease as well as a frequency transition with a temperature increase in the Hodgkin-Huxley (HH) oscillator undergoing saddle homoclinic bifurcations. A gradient of frequency for temperature is derived by perturbation analysis of the stable HH oscillators, in combination with the other gradient of frequency for input current and a so-called phase response curve (PRC) mul...

Abstract This is a study of dynamical system depending on parameter . Under the assumption that has family equilibrium positions or periodic trajectories smoothly , focus details stability loss through various bifurcations (Poincaré–Andronov– Hopf, period-doubling, and so on). Two basic formulations problem are considered. In first, constant subject analysis phenomenon soft h...

We consider a widely used form of models for ship maneuvering, whose nonlinearities entail continuous but nonsmooth second-order modulus terms. For such bifurcations straight motion are not amenable to standard center manifold reduction and normal forms. Based on recently developed analytical approach, we nevertheless determine the character local when stabilizing course with proportional contr...