The numerical approximation of the generalized Lienard equation is considered using delay as parameter. First, the delay difference equation obtained by using Euler method is written as a map.According to the theories of bifurcation for discrete dynamical systems,the conditions to guarantee the existence of Hopf bifurcation for numerical approximation are given. The relations of Hopf bifurcatio...

A tangent double Hopf bifurcation has been found in a rotating cylinder flow driven by the counter-rotation of the top endwall. The codimension-3 tangent double Hopf point has been located using linear stability analysis. The nonlinear analysis of the multiple solutions in a neighborhood of this bifurcation point is performed by numerical solutions of the three-dimensional Navier-Stokes equatio...

This paper deals with an analytical investigation of the nonlinear behavior of an indirect filedoriented control of induction motor. In this context, steady-state solutions in mathematical model of this machine are discussed and an analytical study of the generic codimension one bifurcation, Hopf and Fold bifurcations, was made. Of special interest here is the codimension two bifurcation namely...

A Hopf bifurcation with translational invariance has been widely considered as an appropriate model for the appearance of spiral vortices in counter-rotating Taylor-Couette flow. Our experimental work demonstrates that flow conditions close to the axial boundaries are responsible for the type of bifurcation scenario, i.e., either asymmetric pure traveling waves or more complex behavior, such as...

This paper describes a set of results of detecting nonlinear phenomena appearing in a turbine generator power system with series-capacitor compensation. The analysis was based on the Floquet theory as well as t h e Hopf Bifurcation theorem. After t he first Hopf bifurcation, t he stable limit cycle bifurcates t o a stable torus and a n unstable limit cycle which connects to a stable limit cycle...

Two-dimensional vector fields undergoing a Hopf bifurcation are studied in a Liouville-equation approach. The Liouville equation rules the time evolution of statistical ensembles of trajectories issued from random initial conditions, but evolving under the deterministic dynamics. The time evolution of the probability densities of such statistical ensembles can be decomposed in terms of the spec...

The existence of periodic solutions for evolution equations is of certain interest for both pure and applied mathematicians. Even for bidimensional systems of differential equations the detection of limit cycles by theoretical means is difficult. The bifurcation theory offers a strong tool for finding limit cycles, namely the theory concerning the Hopf bifurcation (when there is a varying param...

IIn this paper, using frequency domain approach, a single mode laser model with delay is investigated. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur when τ passes a sequence of critical values. This means that a family of periodic solutions bifurcate from the equilibrium when the bifurcation parameter exceeds a critical value. Some numerical simulat...

This paper presents qualitative and bifurcation analysis near the degenerate equilibrium in a two-stage cancer model of interactions between lymphocyte cells and solid tumor and contributes to a better understanding of the dynamics of tumor and immune system interactions. We first establish the existence of Hopf bifurcation in the 3-dimensional cancer model and rule out the occurrence of the de...

Abstract. In this paper, we first build up a Westwood+ TCP congestion control model with communication delay in mobile cloud computing networks. We then study the dynamics of this model by analyzing the distribution ranges of eigenvalues of its characteristic equation. Taking communication delay as the bifurcation parameter, we derive the linear stability criteria depending on communication del...