-In this paper a two dimensional chaotic modulator is proposed, based on an electronic controlled Colpitts Oscillator. The modulator is capable of producing constellations of distinct chaotic patterns in a bifurcation diagram, by creating pairs of specific characteristic values. Key-Words: Chaos, Colpitts Oscillator, Modulator, Voltage Controled Oscilator.

In this paper we study the bifurcations of a class of polycycles, called lips, occurring in generic three-parameter smooth families of vector fields on a Möbius band. The lips consists of a set of polycycles formed by two saddle-nodes, one attracting and the other repelling, connected by the hyperbolic separatrices of the saddle-nodes and by orbits interior to both nodal sectors. We determine, ...

Most disease transmission models assume no immunity or permanent immunity for simplicity, however, hosts have temporary immunity for most diseases. In this note we find that the immunity duration is actually the most sensitive parameter for dynamics of disease transmission. We provide numerical schemes to sketch Hopf bifurcations (forward or backward), sensitivity surfaces, periodicity diagrams...

where λ, ε > 0, f is a nonlinear function, and Ω is a smooth bounded domain in Rn. The global bifurcation diagrams and exact multiplicity of equation (1) have been studied in many recent work. In particular, a systematic approach for the positive radially symmetric solutions of (1) when Ω is a ball was presented in Ouyang and Shi [OS1], [OS2] based on previous results by Korman, Li and Ouyang [...

Motivated by numerical examples in solving semilinear elliptic PDEs for multiple solutions, some properties of Newton homotopy continuation method, such as its continuation on symmetries, the Morse index and certain functional structures, are established. Those results provide useful information on selecting initial points for the method to find desired solutions. As an application, a bifurcati...

With a singular perturbation problem occurring in chemical reaction processes, substantial changes of the bifurcation diagram due to discretization are demonstrated. It is shown that a discrete system can possess any number of solutions, whereas the underlying continuous problem has exactly one solution. In addition to that, there is no way to favor one of the various discrete solutions as the ...

We theoretically discuss the impact of the cavity configuration on the possible longitudinal mode multistability in homogeneously broadened lasers. We present a general method allowing to perform a direct bifurcation diagram and to determine the stability of the solutions of a Travelling wave model. We find, in agreement with recent experimental reports, that multistability is more easily reach...

One of the main mechanisms to generate non-stationary data is that the system's environment is always changing with time. It is appropriate to approximate non-stationary time series using the model: X n+1 = F (X n ; U n); where U n is the system's environment at the time n. If the U n is not observable, we may consider to use the model: X n+1 = F (X n ; ^ U n); by somehow learning the function ...

The principal contribution of this article is to determine the existence zones of the various periodic ferroresonant modes (fundamental, harmonic and subharmonic) intervening in the electrical power network. The bifurcation diagrams are used for this purpose. To be able to plot a bifurcation diagram of a particular solution, it is initially necessary to locate this solution and then to follow i...

The dynamic complexities of a prey-predator system in the presence of alternative prey with impulsive state feedback control are studied analytically and numerically. By using the analogue of the Poincaré criterion, sufficient conditions for the existence and stability of semitrivial periodic solutions can be obtained. Furthermore, the corresponding bifurcation diagrams and phase diagrams are i...