The Continuation of Invariant Subspaces (CIS) algorithm produces a smoothly-varying basis for an invariant subspace R(s) of a parameter-dependent matrix A(s). We have incorporated the CIS algorithm into Cl_matcont, a Matlab package for the study of dynamical systems and their bifurcations. Using subspace reduction, we extend the functionality of Cl_matcont to large-scale computations of bifurca...

The use of Pyragas-Type controller proved interest in the stabilization of unstable periodic orbits. The stabilization problem of a balancing inverted pendulum on an horizontally moving cart by the use of such a controller is considered. The main objective of the paper is to propose delayed control law containing only proportional gains able to stabilize the inverted pendulum by avoiding the ex...

A general theory for the study of degenerate Hopf bifurcation in the presence of symmetry has been carried out only in situations where the normal form equations decoupte into phase/amplitude equations. In this paper we prove a theorem showing that in general we expect such degeneracies to lead to secondary torus bifurcations. We then apply this theorem to the case of degenerate Hopf bifurcatio...

It is shown that the logical bases of the static perturbation method, which is currently used in static bifurcation analysis, can also be applied to dynamic bifurcations. A two-time version of the Lindstedt–Poincaré Method and the Multiple Scale Method are employed to analyze a bifurcation problem of codimension two. It is found that the Multiple Scale Method furnishes, in a straightforward way...

Streamline patterns and their local and global bifurcations in a two-dimensional peristaltic flow for an incompressible Newtonian fluid have been investigated. An analytical solution for the stream-function is found under a long-wavelength and low-Reynolds number approximation. The problem is solved in a moving coordinate system where a system of nonlinear autonomous differential equations can ...

Instabilities and pattern formation in buoyant-thermocapillary flows have been extensively studied in the last years. Classically heat is applied uniformly from below [1] where the conductive solution becomes unstable for temperature gradients beyond a certain threshold. A more general set-up considers thermoconvective instabilities when a basic dynamic flow is imposed through non-zero horizont...

We consider a general class of first-order nonlinear delay-differential equations (DDEs) with reflectional symmetry, and study completely the bifurcations of the trivial equilibrium under some generic conditions on the Taylor coefficients of the DDE. Our analysis reveals a Hopf bifurcation curve terminating on a pitchfork bifurcation line at a codimension two Takens–Bogdanov point in parameter ...

The main purpose of this paper is to give a reasonably comprehensive discussion of what is commonly referred to as the bifurcation analysis applied to an indirect field oriented control of induction machines (IFOC). In the current work, we study the appearance of self-sustained oscillations in AC drives and compute their corresponding stability margins. As the dynamics is explored, a transition...