Hopf bifurcations in an extended Lorenz system

Bifurcations of Fractional-order Diffusionless Lorenz System

Using the predictor-corrector scheme, the fractional-order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional-order diffusionless system for variation of the single control parameter is determined. The route to chaos is by period-doubling bifurcation in this fractional-order system, and some typical bifurcations are observed, such as the flip ...

Attractors and Bifurcations of the Stochastic Lorenz System

This paper discusses the well known Lorenz system under the in-uence of white noise. We prove the existence of a unique solution, a stationary distribution and a random attractor. Furthermore, the random attractor contains for particular parameters only one point. Numerical experiments illustrate the results.

Discretizing Dynamical Systems with Hopf-Hopf Bifurcations

We consider parameter-dependent, continuous-time dynamical systems under discretizations. It is shown that Hopf-Hopf bifurcations are O(h)-shifted and turned into double Neimark-Sacker points by general one-step methods of order p. Then we discuss the effect of discretization methods on the emanating Hopf curves. The numerical approximation of the critical eigenvalues is analyzed too. The resul...

Double Hopf Bifurcations

Hopf Bifurcations in Cancer Models

The purpose of the present paper is to prove that there are nonconstant periodic integral curves of a mathematical model of cancer growth. We shall prove, there are Hopf bifurcations in the mathematical model and that the oscillating solutions are uniformly, asymptotically stable.