Complex dynamics in the reduced swing equations of a power system are investigated. As the change of bifurcation parameter μ, the system exhibits complex bifurcations, such as saddle-node bifurcation, Hopf bifurcation, cyclic fold bifurcation and torus bifurcations and complex dynamics, such as periodic orbits, quasiperiodic orbits, period-doubling orbits and chaotic attractors which link with ...

A general explicit formula is derived for controlling bifurcations using nonlinear state feedback. This method does not increase the dimension of the system, and can be used to either delay (or eliminate) existing bifurcations or change the stability of bifurcation solutions. The method is then employed for Hopf bifurcation control. The Lorenz equation and Rössler system are used to illustrate ...

We study some periodic and quasiperiodic behaviors exhibited by the Chua’s equation with a cubic nonlinearity, near a Hopf–pitchfork bifurcation. We classify the types of this bifurcation in the nondegenerate cases, and point out the presence of a degenerate Hopf–pitchfork bifurcation. In this degenerate situation, analytical and numerical study shows a diversity of bifurcations of periodic orb...

In this paper we extract and visualize the topological skeleton of two-parameter-dependent vector fields. This kind of vector data depends on two parameter dimensions, for instance physical time and a scale parameter. We show that two important classes of local bifurcations – fold and Hopf bifurcations – build line structures for which we present an approach to extract them. Furthermore we show...

A normal form is derived for Hamiltonian–Hopf bifurcations of solitary waves in nonlinear Schrödinger equations with general external potentials. This normal form is a simple second-order nonlinear ordinary differential equation (ODE) that is asymptotically accurate in describing solution dynamics near Hamiltonian–Hopf bifurcations. When the nonlinear coefficient in this normal form is complex,...

To understand joint effects of logistic growth in target cells and intracellular delay on viral dynamics in vivo, we carry out two-parameter bifurcation analysis of an in-host model that describes infections of many viruses including HIV-I, HBV and HTLV-I. The bifurcation parameters are the mitosis rate r of the target cells and an intracellular delay τ in the incidence of viral infection. We d...

Functional connectivity is a fundamental property of neural networks that quantifies the segregation and integration of information between cortical areas. Due to mathematical complexity, a theory that could explain how the parameters of mesoscopic networks composed of a few tens of neurons affect the functional connectivity is still to be formulated. Yet, many interesting problems in neuroscie...

This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics which is fairly rich. The neural system exhibits a unique rest point or three ones for the different values of coupling strength by employing t...

The nonlinear dynamics of Taylor-Couette flow in a small aspect ratio annulus (where the length of the cylinders is half of the annular gap between them) is investigated by numerically solving the full three-dimensional Navier-Stokes equations. The system is invariant to arbitrary rotations about the annulus axis and to a reflection about the annulus half-height, so that the symmetry group is S...

A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory ...