In this paper, we show numerically that the so-called HIV therapy system is regular and converges to a stable equilibrium point for most realistic values (in the medical sense) of its bifurcation parameters. Although there is no rigorous proof of this convergence property, it is conjectured that the system is not chaotic for all positive bifurcation parameters.

We carry out the global bifurcation analysis of the classical Lorenz system. For many years, this system has been the subject of study by numerous authors. However, until now the structure of the Lorenz attractor is not clear completely yet, and the most important question at present is to understand the bifurcation scenario of chaos transition in this system. Using some numerical results and o...

Homoclinic snaking refers to the bifurcation structure of symmetric localised roll patterns that are often found to lie on two sinusoidal “snaking” bifurcation curves, which are connected by an infinite number of “rung” segments along which asymmetric localised rolls of various widths exist. The envelopes of all these structures have a unique maximum and we refer to them as symmetric or asymmet...

We give an explicit construction of families of Dm-equivariant polynomial vector fields in R possessing a codimension-one homoclinic cycle. The homoclinic cycle consist of m homoclinic trajectories all connected to the equilibrium at the origin. The constructed vector fields can provide a setting for a (numerical) bifurcation study of these homoclinic cycles, in particular for m a multiple of f...

We prove the existence of a global bifurcation branch of 2π-periodic, smooth, traveling-wave solutions of the Whitham equation. It is shown that any subset of solutions in the global branch contains a sequence which converges uniformly to some solution of Hölder class C, α < 1 2 . Bifurcation formulas are given, as well as some properties along the global bifurcation branch. In addition, a spec...

In this Letter, a four-neuron BAM neural network with four time delays is considered, where the time delays are regarded as parameters. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic equation, it is found that Hopf bifurcation occurs when these delays pass through a sequence of critical value. A formula for determini...